# International Journal of Robust and Nonlinear Control

Published by Wiley

Online ISSN: 1099-1239

Print ISSN: 1049-8923

Published by Wiley

Online ISSN: 1099-1239

Print ISSN: 1049-8923

Publications

A DC-to-AC power conversion scheme is presented which uses a
conventional DC-to-DC switched power converter of the
“boost” type. The control scheme is constituted by a sliding
mode controller which indirectly tracks a suitable inductor current
reference trajectory resulting in a corresponding tight approximation to
the desired AC capacitor voltage as the corresponding trajectory for the
ideal sliding dynamics. The differential flatness property of the
“boost” converter allows one to approximately express the
(input) inductor current reference trajectory in terms of a static
nonlinear differential function of the (output) desired capacitor
voltage AC signal. The AC signal generation features of the approach are
demonstrated on a biased sinusoidal signal but, in fact, any
sufficiently biased differentiable voltage reference signal is
achievable in principle. This approximate differential relation between
the reference current and the desired voltage is obtained as the outcome
of a rapidly convergent offline iterative procedure devised as part of a
trajectory planning task (only one or two iterations are sufficient to
obtain a remarkable precision). Simulation results are presented for the
first few sliding surface candidates obtained from the proposed
algorithm

…

In this paper, we study the problem of disturbance attenuation by output feedback for linear systems subject to actuator saturation. A nonlinear feedback control law, expressed in the form of a quasi-LPV system with state dependent scheduling parameter, is constructed that leads to the attenuation of the effect of the disturbance on the output of the system. The level of disturbance attenuation is measured in terms of the restricted L 2 gain and the restricted L 2 to L ∞ gain over a set of bounded disturbances.

…

A strategy is proposed for fault-tolerant control system (FTCS)
design using multiple controllers. The design of such multiple
controllers is shown to be unique in the sense that the resulting
control system does neither have the problem of conservativeness of
conventional passive fault-tolerant control (FTC) nor the risk of
instability associated with active FTCS in case of an incorrect fault
detection and isolation (FDI) decision. In other words, the stability of
the closed-loop system is always ensured regardless the FDI decisions.
The correct FDI decision will further lead to optimal performance of the
system. The paper presents an interesting way to deal with the
conflicting requirements among stability, redundancy, and graceful
degradation in performance for fault-tolerant control systems. Detailed
design procedure has been presented with consideration of possible
parameter uncertainties

…

We study controller synthesis for systems subject to actuator magnitude and rate saturation constraints, where each actuator has a dynamic model of order at least one. The solvability conditions are expressed as finite-dimensional linear matrix inequalities. Disturbance attenuation in terms of the energy-to-peak gain from the disturbance to the controlled output is considered, though other performance measures are also possible. The results apply to the more general case of systems under actuator and state constraints.

…

A new approach employing both adaptive and robust methodologies is
proposed for stick-slip friction compensation for tracking control of an
one-DOF DC-motor system. It is well-known that the major components of
friction are Coulomb force, viscous force, exponential force (used to
model the downward bend of friction at low velocity) and
position-dependent force. Viscous force is linear and Coulomb force is
linear in parameter; thus, these two forces can be compensated by
adaptive feedforward cancellation. Meanwhile, the latter two forces,
which are neither linear nor linear in parameters, can only be partially
compensated by feedforward cancellation. Therefore, a robust compensator
with an embedded adaptive law to online “learn” the upper
bounding function is proposed to compensate the uncanceled exponential
and position-dependent friction. Lyapunov's direct method is utilized to
prove the globally asymptotic stability of the servo-system under the
proposed friction compensation method

…

The control of an aircraft encountering windshear after takeoff is
treated as a problem of stabilizing the climb rate about a desired
value. An adaptive strategy is developed which uses only climb rate
information. Robustness vis-a-vis windshear structure and intensity is
illustrated via simulations employing four different windshear models.
Simulations were carried out for a Boeing-727 aircraft with three
JT8D-17 turbofan engines

…

In this paper, we present a unified approach of direct adaptive motion control laws for robot manipulators that have been studied during the last years by several authors. It provides a general approach based on passivity to demonstrate global asymptotic stability of adaptive schemes applied to rigid multilinked manipulators. It is shown that most of the schemes fit within this framework, which presents the advantage of being more systematic than other techniques and therefore will enable a unified presentation of the several schemes proposed to date and will increase our understanding of adaptive control of robot manipulators.

…

Hysteresis switching adaptive control systems designed using certain types of L 2e -gain type cost functions are shown to be robustly stabilizing if and only if certain plant-independent conditions are satisfied by the candidate controllers. These properties ensure closed-loop stability for the switched multi-controller adaptive control (MCAC) system whenever stabilization is feasible. The result is a safe adaptive control system that has the property that closing the adaptive loop can never induce instability provided only that at least one of the candidate controllers is capable of stabilizing the plant.

…

This paper considers the problem of fault detection and isolation in continuous- and discrete-time systems while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems together with methods for appropriate design of observer based fault detectors. The -step delayed fault detection problem is also considered for discrete-time systems. Moreover, certain indirect fault detection methods such as unknown input observers, eigenstructure assignment, factorization, and parity equation approaches are generalized by including the almost estimation methods in addition to exact estimation methods. Copyright

…

For both continuous-time and discrete-time systems, the authors
establish the necessary and sufficient conditions under which an H<sub>2
</sub> almost disturbance decoupling problem with internal stability is
solvable by proper controllers and/or strictly proper controllers

…

The frequency domain design of robust feedback control systems involves the fitting of a designable complex function of frequency to specification/uncertainty derived constraints. At present there are two basically different approaches to these problems: the several gain vs. frequency approaches and the two gain-phase vs. frequency approaches. Unfortunately, the commonalities, advantages and disadvantages of these approaches are not widely appreciated. In this paper the authors develop a common framework for examining these alternatives and use this framework to reveal some of their similarities, strengths and weaknesses.

…

Develops a fixed-architecture controller analysis and synthesis
framework that addresses the problem of multivariable linear
time-invariant systems subject to plant input and output nonlinearities
while accounting for robust stability and robust performance over the
allowable class of nonlinearities. The proposed framework is based on
the classical Lur'e problem and related Aizerman conjecture concerning
the stability of a feedback loop involving a sector-bounded
nonlinearity. Specifically, the authors extend the classical notions of
absolute stability theory to guarantee closed-loop stability of
multivariable systems in the presence of input nonlinearities. In order
to capture closed-loop system performance the authors also consider the
minimization of a quadratic performance criterion over the allowable
class of input nonlinearities. The principal result is a set of
constructive sufficient conditions for absolute stabilization
characterized via a coupled system of algebraic Riccati and Lyapunov
equations

…

In this paper we develop an optimality-based framework for
backstepping controllers. Specifically, using a nonlinear-nonquadratic
optimal control framework we develop a family of globally stabilizing
backstepping controllers parametrized by the cost functional that is
minimized. Furthermore, it is shown that the control Lyapunov function
guaranteeing closed-loop stability is a solution to the steady-state
Hamilton-Jacobi-Bellman equation for the controlled system and thus
guarantees both optimality and stability. The results are specialized to
the case of integrator backstepping

…

The rotational/translational actuator (RTAC) provides a
low-dimensional nonlinear system for investigating nonlinear control
techniques. The lossless formulation of this problem involves coupling
of an undamped oscillator with a rotational rigid body mode.
Stabilization and disturbance rejection objectives for this problem have
been formulated as a benchmark problem. We implement four nonlinear
controllers on the RTAC, including an integrator backstepping controller
and three passivity-based controllers. The integrator backstepping
design is based on the work of Wan et al. (1996). This approach requires
that the equations of motion be reformulated by partial feedback
linearization. Integrator backstepping is then used to produce a family
of globally asymptotically stabilizing control laws. Next, three
passivity-based controllers are developed for the RTAC. These
controllers have intuitively appealing energy-dissipative properties and
thus also inherent stability robustness to plant and disturbance
uncertainty. Two of these controllers are encompassed by the classical
passivity framework. The final controller is based upon the novel
concept of resetting absorbers

…

A global optimization algorithm for solving bilinear matrix
inequalities (BMI) problems is developed. It is based on a dual Lagrange
formulation for computing lower bounds that are used in a branching
procedure to eliminate partition sets in the space of nonconvex
variables. The advantage of the proposed method is twofold. First, lower
bound computations reduce to solving easily tractable linear matrix
inequality (LMI) problems. Secondly, the lower bounding procedure
guarantees global convergence of the algorithm when combined with an
exhaustive partitioning of the space of nonconvex variables. Another
important feature is that the branching phase takes place in the space
of nonconvex variables only, hence limiting the overall cost of the
algorithm. Also, an important point in the method is that separated LMI
constraints are encapsulated into an augmented BMI for improving the
lower bound computations. Applications of the algorithm to robust
structure/controller design are considered

…

The computation of the general structural singular value (μ) is
NP hard. Therefore, quick solutions to medium sized problems must often
be approximate. In many of the cases where the current approximate
methods are unsatisfactory, improved solutions can be obtained. It is
shown that, despite its combinatoric nature, branch and bound techniques
can give substantially improved solutions with only moderate
computational cost

…

This article concerns piecewise linear systems and determining if
they meet given H<sup>∞</sup> performance specifications. Such
problems occur in control of linear systems with saturation
nonlinearities. While one could imagine many mathematically natural
piecewise linear systems problems we took care to extract one which does
correspond to control of saturated plants. We think many such problems
will fall into the category treated here. After a serious compromise
(which makes our test for meeting specifications conservative), we
arrive at a type of piecewise Riccati equation. Even these look
formidable, however we begin a study of them

…

In this paper, it is shown how derivative bounds on uncertain
time-varying parameters can be exploited in robustness analysis of
linear systems. A new stability criterion is derived, based on integral
quadratic constraints in the frequency domain. The new stability
criterion interpolates between well known robust stability results,
which are obtained in the limit. As the derivative bounds tend to zero,
the new criterion turns into the usual upper bound for the structured
singular value. The stability analysis, which involves a search for
suitable multipliers, can be formulated as a convex optimization problem
in terms of linear matrix inequalities

…

We derive bounds on the parameters of systems represented by a transfer functions such that any system satisfying these bounds will satisfy a bound on the H<sub>∞</sub>-norm of the difference between this transfer function and a nominal one. We develop the bound and give examples for illustration

…

We develop a graphical stability criterion using a Nichols chart rather than the standard complex plane. The motivation for this development is that use of Nichols charts can often simplify control design. Chief among the techniques that employ Nichols charts is the quantitative feedback theory (QFT). Numerous examples have demonstrated that the design procedure used in single-input, single-output QFT does indeed lead to a stable design and even to robust stability in the case of uncertain plants. However, a rigorous proof for the stability of this and, for that matter, of any other Nichols chart-based techniques has never been formulated. Indeed, in Reference 2, it was remarked that in some cases it may be difficult to define closed-loop stabilizing using Nichols plots. In this note we present a simple and natural proof that is based on the celebrated Nyquist criterion. In either continuous time or discrete time, the new criterion is illustrated with several examples, and extended to a class of uncertain systems.

…

In this paper we propose a new self-tuning type variable structure
control (VSC) method for a class of nonlinear dynamical systems with
parametric uncertainties. The control law is designed to satisfy the
sliding mode condition while the online parameter identification is
incorporated in the control system. Necessary modifications are made for
the parameter identification to avoid the singularity of control input.
By virtue of sliding mode, the proposed identification algorithm can be
applied to those nonlinear systems which may not be linear in parametric
space but are linear while in sliding mode. A model-based strategy is
further introduced to estimate the uncertainty bound. The new approach
attains the gain scheduling property by tuning the switching gain in
accordance with the estimated system uncertainties, that is, the
switching gain tends to reduce asymptotically while ensuring that the
sliding mode condition is maintained

…

Considers robust stability analysis and synthesis problems for
closed loop vibrational control. In the analysis problem, the authors
derive an upper bound on the allowable unstructured uncertainty, which
preserves the stability of a closed loop vibrationally stabilized
system. In the synthesis problem, the authors establish a necessary and
sufficient condition for the existence of a single vibrational
controller that stabilizes a polytope of plants

…

In this work we investigate a new approach for stabilizing nonlinear systems using sliding mode control. The idea behind this method is the following: given an approximately feedback linearizable system, we define a local coordinate transformation and then find a sliding mode controller, in the new coordinates, which steers the state to the origin. Our results are compared to those obtained using approximate feedback linearization-based sliding mode control. Copyright (C) 2007 John Wiley & Sons, Ltd.

…

A general framework for designing nonlinear fixed order (i.e.,
full- and reduced-order) dynamic passive controllers for passive systems
is developed using nonlinear dissipation theory. Specifically, by
extending linear passive controller synthesis frameworks a family of
globally asymptotically stabilizing nonlinear passive controllers is
developed that can serve to enhance system performance and energy
dissipation. The proposed approach is applied to the
rotational/translational proof mass actuator nonlinear benchmark problem
to develop fixed-order dynamic output feedback nonlinear controllers

…

This paper considers the problem of robust performance of a linear
time-invariant system in ℋ<sub>∞</sub> norm. The concepts of
complex and real performance radii are introduced to describe the
smallest size of dynamic or parametric perturbations to a feedback
system that either destabilize the system or destroy a performance bound
in certain closed loop transfer matrix of the system. An algorithm to
compute the complex performance radius is given. For the real
performance radius, a lower bound, which often turns out to be exact, is
obtained

…

This paper presents an explicit noniterative method for computing
the positive real matrices and Youla's spectral factorization of an MIMO
strictly positive real system. All the computations are performed based
on a minimal state space realization (A, B, C, D) with no restriction on
D. The algorithm is tested on a seventh order MIMO system

…

A set of integral quadratic constraints (IQC) is derived for a
class of “rate limiters”, modelled as a series connections
of saturation-like memoryless nonlinearities followed by integrators.
The result, when used within the standard IQC framework, is expected to
be widely useful in nonlinear system analysis. For example, it enables
“discrimination” between “saturation-like” and
“deadzone-like” nonlinearities and can be used to prove
stability of systems with saturation in cases when replacing the
saturation block by another memoryless nonlinearity with equivalent
slope restrictions makes the whole system unstable. In particular, it is
shown that the L<sub>2</sub> gain of a unity feedback system with a rate
limiter in the forward loop cannot exceed √2

…

In this paper we study discrete-time linear systems with full or partial constraints on both input and state. It is shown that the solvability conditions of stabilization problems are closely related to important concepts, such as the right-invertibility of the constraints, the location of constraint invariant zeros and the order of constraint infinite zeros. The main results show that for right-invertible constraints the order of constrained infinite zeros cannot be greater than one in order to achieve global or semi-global stabilization. This is in contrast to the continuous-time case. Controllers for both state feedback and measurement feedback are constructed in detail. Issues regarding non-right invertible constraints are discussed as well.

…

A successful controller design paradigm must take into account
both model uncertainty and design specifications. In this paper we
propose a design procedure, based upon the use of convex optimisation,
that takes explicitly into account both time and frequency domain
specifications. The main result of the paper shows that these
controllers can be obtained by solving a sequence of problems, each one
consisting of a finite-dimensional convex optimization and a standard,
unconstrained ℋ<sub>∞</sub> problem. Additionally, the paper
serves as a brief tutorial on the issues involved in addressing design
problems with multiple design specifications via convex optimization

…

Presented is a nonlinear controller design methodology for a class
of regulating systems subjected to quantitative time domain constraints.
The output and actuator saturation performance specifications are given
as allowable time domain tolerances. The controller design is executed
in the frequency domain and is applicable when the frequency response of
a linear design cannot satisfy the gain and phase characteristics
required by quantitative time domain specifications. A describing
function (DF) approach, automated by the Volterra series, facilitates
the nonlinear controller design. The resulting gain and phase
distortions associated with the DF of the dynamic nonlinear element are
used to achieve the desirable open loop gain and phase characteristics
identified by the time domain constraints. The design methodology is
illustrated on the idle speed control of a Ford 4.6L V-8 fuel injected
engine. The engine input is the by-pass air valve and the regulated
output is engine speed. The power steering pump generates the
nonmeasureable external torque load

…

Reference governors for discrete-time linear systems with state
and control constraints are considered. The governors attenuate, but
only when necessary, the reference inputs to the linear system so that
the constraints are enforced and the system maintains it desirable
linear behavior in the presence of nonlinear effects such as actuator
saturation. Results of Gilbert and Kolmanovsky (1994) are extended in
significant ways. It is possible to treat disturbance inputs and provide
flexibility in the choice of the nonlinear function that determines the
operation of the reference governor. It is proved that constraint
satisfaction is guaranteed for all reference inputs and disturbance
inputs. Moreover, under reasonable conditions on the reference input,
the eventual action of the reference governor is a unit delay. An
example, which illustrates the results of the paper, is given. It shows,
among other things, that high sample rates need not increase the
complexity of an effective reference governor

…

The problem of closed-loop approximation of a continuous-time
controller by a low order discrete-time controller is investigated. The
operator representing the error in approximation can be approximated
(arbitrarily closely) by a time-invariant discrete-time system resulting
from applying fast sampling and lifting. We propose a method for
obtaining a low-order discrete-time controller which makes small the
approximation error based on recasting the approximation problem as a
four-block H<sub>∞</sub> problem

…

This paper presents an application of H<sub>∞</sub> and
μ-synthesis controller design methods to a coal-fired power
generation unit and compares the closed loop performance and robustness
of H<sub>∞</sub> and μ-synthesis control laws with those of an
H<sub>2</sub> control law. All three controller synthesis procedures are
applied to a two-input two-output plant model which has time delay,
differential part, colored noise output disturbance and sensor noise
disturbance. Application of the procedures to the model shows that when
the shape of the closed loop control signals of all three designs Is
closely matched, in the low frequency range the μ-synthesis and
H<sub>∞</sub> control laws have robustness much better than that
of H<sub>2</sub> control law, while providing adequate robustness in the
high frequency range. H<sub>∞</sub> control law gives the best
performance, and H<sub>2</sub>-the worst of the three designs,
exhibiting the largest overshoot. The balancing procedure permits
significant reduction of the order of the controllers without
degradation in performance and robustness. The comparative evaluation of
three designs shows that in power plant control problem H<sub>∞
</sub> and μ-synthesis designs provide much more consistent and
convenient performance/robustness trade-off than H<sub>2</sub> design

…

We consider the theoretical aspects of the control problem for
robots with rigid links which consist of some rigid joints and some
non-negligible elastic joints. We start from the reduced model of robots
with all elastic joints introduced by Spong, which is linearizable by
static feedback (as for the rigid robot model). For the mixed
rigid/elastic joints, we give the structural necessary and sufficient
conditions for input-output decoupling and full state linearization via
static state feedback. These turn out to be very restrictive. However,
when a robot fails to satisfy these conditions, we show that a dynamic
state feedback always guarantees the same result. This implies that, for
the mixed rigid/elastic joint case, the role of dynamic feedback is
essential. The explicit forms of the needed nonlinear controllers are
provided in terms of the dynamic model elements

…

This paper considers the problem of output-feedback guaranteed
cost controller design for uncertain time-delay systems The uncertainty
in the system is assumed to be norm-bounded and time-varying. The
time-delay is allowed to enter the state and the measurement equations.
It is proved that the existence of the guaranteed cost controller is
equivalent to the feasibility of certain matrix inequalities. A
numerical algorithm is developed to construct a full order
output-feedback controller that minimizes a specific cost bound for a
quadratic performance index

…

In this paper, constructive control techniques have been proposed for controlling strict feedback (lower triangular form) nonlinear systems with a time-varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. Based on the using of a linear dynamic high gain observer in combination with a linear dynamic high gain controller, the delay-independent output feedback controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed

…

A discretized Lyapunov functional method for systems with multiple
delay is refined. The main ideas used are variable elimination and
integral inequality. The resulting new stability criterion is simpler.
Numerical examples indicate that the new method is much less
conservative for a given discretization mesh. In most applications, it
appears that a most coarse discretization mesh compatible with the
delays is sufficient

…

We consider the problem of designing encoders, decoders and controllers which stabilize feed forward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilization of the closed-loop system. The analysis rests on the stability properties of a class of cascade impulsive time-delay systems.

…

This paper addresses the reduced-order H∞ filter design for linear time varying discrete-time systems in which all measurements are not noise-free. The proposed filter has a Luenberger observer structure and its order is n - p, where n and p are the order of signal systems and the number of measurements, respectively. Several bounded real lemmas are developed and they are the only tools used to establish the reduced-order filter design in this paper. It is shown that the full order a priori and a posteriori filters can be obtained by properly choosing the filter order and parameters based on the reduced-order filter design results. The resultant filters are the same as the known full-order optimal H∞ filters for time-invariant systems.

…

This paper extends the Riccati equation approach to quadratic stabilizability of an uncertain system. The main result gives a guaranteed cost control which is in a sense optimal with respect to a quadratic cost index.

…

This paper considers the application of the skewed structured singular value to the robust stability of systems subject to strictly real parametric uncertainty. Three state-space formulations that counteract the discontinuous nature of this problem are detailed. It is shown that the calculation of the supremum of the structured singular value over a frequency range using these formulations transforms into a single skewed structured singular value calculation. Like the structured singular value, the calculation of the exact value of the skewed structured singular value is a NP-hard problem, therefore alternative, less computationally demanding algorithms to determine upper and lower bounds are necessary. Two algorithms that determine upper and lower bounds on the skewed structured single value are presented. These algorithms are critically assessed by performing a robust stability analysis on a safety-critical experimental drive-by-wire vehicle.

…

In this paper, we develop new results concerning the
risk-sensitive dual control problem for output feedback nonlinear
systems, with unknown time-varying parameters. A dynamic programming
equation solution is given to an optimal risk-sensitive dual control
problem penalizing outputs, rather than the states, for a reasonably
general class of nonlinear signal models. This equation, in contrast to
earlier formulations in the literature, clearly shows the dual aspects
of the risk-sensitive controller regarding control and estimation. The
extensive computational burden for solving this equation motivates our
study of risk-sensitive versions for one-step horizon cost indices and
suboptimal risk-sensitive dual control. The idea of a more generalized
optimal risk-sensitive dual controller is briefly introduced

…

This paper is concerned with a walking robot with knees on level ground imitating the passive walking on a given slope. Basic principle of a proposed control method is that dynamics of the active walking robot is matched to that of the passive walking one. However, since it is hard for the knee-jointed walking robot to successively or robustly realize a stable passive walking on the downhill slope, the passive walking robot is first actively controlled to continue to walk with an actuator at the hip. Then the dynamics of the walking robot on the level grand is matched to that of the stabilized passive walking robot on the slope by implementing actuators at the ankles as well as at the hip. Copyright

…

In this paper we develop optimal output feedback controllers for set-point regulation of linear nonnegative dynamical systems. Specifically, using a constrained fixed-structure control framework we develop optimal output feedback control laws that guarantee that the trajectories of the closed-loop system remain in the nonnegative orthant of the state space for nonnegative initial conditions. In addition we characterize domains of attraction predicated on closed and open Lyapunov level surfaces contained in the nonnegative orthant for unconstrained optimal linear-quadratic output feedback controllers. Output feedback controllers for compartmental systems with nonnegative inputs are also given.

…

An aircraft's response to control inputs varies widely throughout
its flight envelope. The aircraft configuration also impacts control
response through variations in center of gravity and moments of inertia.
Hence, designing a flight control system (FCS) to accommodate the full
flight envelope and configuration set of an aircraft is clearly a
complex undertaking. Quantitative feedback theory (QFT) is a robust
control design method which provides an avenue of approach to
full-envelope flight control design. Furthermore, a QFT-based design
method gives the engineer direct control over compensator order and
gain. In this paper, a full subsonic flight envelope FCS is designed for
the VISTA F-16 aircraft using QFT for four representative aircraft
configurations. In addition, flying qualities are imbedded in the
longitudinal design by using a control variable which varies with the
aircraft's energy state throughout the flight envelope. This variable is
a linear combination of the aircraft's pitch channel states and is
synthesized to closely reflect the actual control desires of the pilot
throughout the aircraft flight envelope. The strict control of the
compensator order and gain allowed by QFT facilitates the attainment of
desired performance while avoiding physical actuator saturations. Linear
simulations with realistically large control inputs are used to validate
the design

…

It is well known that in systems described by Euler-Lagrange
equations the stability of the equilibria is determined by the potential
energy function. Further, these equilibria are asymptotically stable if
suitable damping is present in the system. These properties motivated
the development of a passivity-based controller design methodology which
aims, at modifying the potential energy of the closed loop and the
addition of the required dissipation. To achieve the lattice objective
measurement of the generalized velocities is typically required. Our
main contribution in this paper is the proof that damping injection
without velocity measurement is possible via the inclusion of a dynamic
extension provided the system satisfies a dissipation propagation
condition. This allows us to determine a class of Euler-Lagrange systems
that can be globally asymptotically stabilized with dynamic output
feedback. We illustrate this result with the problem of set-point
control of elastic joints robots. Our research contributes, if modestly,
to the development of a theory for stabilization of nonlinear systems
with physical structures which effectively exploits its energy
dissipation properties

…

The authors provide an alternative solution to the problem of
semiglobal stabilization of a class of minimum phase nonlinear systems
that was considered by A.R. Teel (1991). The method used yields a
stabilizing linear state feedback law in contrast to a nonlinear state
feedback law proposed by Teel. The peaking phenomenon is eliminated by
inducing a specific time-scale structure in the linear part of the
closed-loop system. This structure consists of a very slow and a very
fast time scale. The crucial component in the method is the relation
between the slow and the fast time-scales. The proposed linear state
feedback control law has a single tunable gain parameter that allows for
local asymptotic stability and regulation to the origin for any initial
condition in some a priori given (arbitrarily large) bounded set

…

In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.

…

This paper considers the problem of optimal guaranteed cost
control of an uncertain system via output feedback. The uncertain system
under consideration contains a single uncertainty block subject to an
integral quadratic constraint. The cost function considered is a
quadratic cost function defined over an infinite time interval. The main
result of the paper gives a necessary and sufficient condition for the
existence of a guaranteed cost controller guaranteeing a specified level
of performance. This condition is given in terms of the existence of
suitable solutions to an algebraic Riccati equation and a Riccati
differential equation. The resulting guaranteed cost controller is in
general time-varying

…

In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman-Bucy filter

…

Top-cited authors