P. Bolzern

Politecnico di Milano, Milano, Lombardy, Italy

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Publications (92)83.53 Total impact

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    ABSTRACT: This paper investigates on the stability properties of Positive Markov Jump Linear Systems (PMJLS’s), i.e. Markov Jump Linear Systems with nonnegative state variables. Specific features of these systems are highlighted. In particular, a new notion of stability (Exponential Mean stability) is introduced and is shown to be equivalent to the standard notion of 1-moment stability. Moreover, various sufficient conditions for Exponential Almost-Sure stability are worked out, with different levels of conservatism. The implications among the different stability notions are discussed. It is remarkable that, thanks to the positivity assumption, some conditions can be checked by solving Linear Programming feasibility problems.
    Automatica. 01/2014;
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    European Journal of Control 07/2013; 6(1):89–92. · 1.25 Impact Factor
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    P. Bolzern, P. Colaneri, G. De Nicolao
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    ABSTRACT: Adaptive filtering of a scalar signal corrupted by noise is considered. In particular, the signal to be estimated is given as a linear regression model depending on a drifting parameter. The mean-square and worst-case performances of the H∞-adaptive filter are studied. Bounds for the mean-square performance are established on the basis of upper bounds for the solution of the relevant Riccati equation. As for the worst-case performance, it is shown that an H∞-.filter designed with a certain value of the parameter γ ensures an easy-to-compute attenuation level less than γ.
    European Journal of Control 07/2013; 6(1):78–88. · 1.25 Impact Factor
  • P. Bolzern, P. Colaneri, G. De Nicolao
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    ABSTRACT: The technical note studies a class of linear systems whose piecewise-constant dynamic matrix is subject to both stochastic jumps, governed by a Markov chain, and deterministic switches. These systems will be dubbed switching dynamics Markov jump linear systems (SD-MJLS). Sufficient conditions for exponential almost sure stability (EAS-stability) are established under either hard or average constraints on the dwell-time between switching instants. The proof relies on easy-to-check norm contractivity conditions and the ergodic law of large numbers.
    IEEE Transactions on Automatic Control 01/2013; 58(1):209-214. · 2.72 Impact Factor
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    ABSTRACT: This paper generalises the Small Gain Theorem – SGT to cope with switched linear systems. A switching strategy able to guarantee stability of the feedback interconnection of a switching linear subsystem and a linear stable norm-bounded perturbation is developed. The new version of SGT is specially important to solve two different problems. The first one concerns the possibility of enhancing the robustness of a feedback control system by appropriately orchestrating the switches among a set of given linear regulators. The second problem is the design of a stabilising switching strategy for time-delay switched systems. Both cases of state and output feedback switching laws are considered. Remarkably, since the sufficient conditions for the existence of a solution are delay-dependent, they are less conservative with respect to previous results in the literature. The theory is illustrated by means of academic examples.
    International Journal of Control 01/2013; 86(6). · 1.01 Impact Factor
  • Paolo Bolzern, Patrizio Colaneri
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    ABSTRACT: This paper deals with the analysis of stability and the characterisation of input–output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H 2 and H ∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.
    International Journal of Control 01/2013; 86(7). · 1.01 Impact Factor
  • L. Galbusera, P. Bolzern
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    ABSTRACT: In this paper we propose contributions on the control of switched linear systems subject to time-delays. Our methods allow to synthesize state feedback switching laws able to ensure the stabilization and the fulfillment of a prescribed ℌ∞ disturbance attenuation property. The proposed criteria are delay-dependent and based on an application of the descriptor approach, previously introduced in the literature to study standard time-delay systems. The core of our procedure is based on the solution of sets of matrix inequalities, which allow simultaneously to assign a suitable switching law and to determine a feasible piecewise quadratic Lyapunov-Krasovskii functional associated to it.
    Control Conference (ECC), 2013 European; 01/2013
  • P. Bolzern, P. Colaneri
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    ABSTRACT: This paper deals with the analysis of stability and the characterization of input-output norms for dual switching linear systems in discrete-time. These systems are subject to two independent switching signals, taking values in finite sets, coming from different sources. The first switching signal is periodic while the second is uncontrolled and generate parameter jumps which are either completely arbitrary or satisfy a prescribed dwell-time constraint. The overall system is a linear time-varying system exhibiting a complex dynamic behavior due to the interplay between the periodic switches and the uncontrolled jumps. LMI conditions for stability and guaranteed H2 norm input/output performances are provided. The results are obtained by merging the theory of linear periodic systems with recent developments on switched linear time-invariant systems.
    Control Conference (ECC), 2013 European; 01/2013
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    ABSTRACT: A passive system with positive definite storage function is not only stable but is intrinsically robustly stable with respect to a wide class of feedback disturbances. For linear time invariant systems, passivity can be characterized either in time domain or in frequency domain from positive realness. This paper aims to generalize this concept to continuous-time switched linear systems. Analysis is performed by taking into account state dependent and arbitrary time dependent switching functions with a prescribed dwell time. A control design problem related to the determination of a switching strategy, based upon output measurements, that renders a switched linear system passive is also considered. The methods introduced in the paper can be effectively applied to the control of the duty cycle and passivation of switched circuits.
    Systems & Control Letters 04/2012; 61(4):549–554. · 1.67 Impact Factor
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    ABSTRACT: This paper generalizes the Small Gain Theorem - SGT to cope with time-delay switched linear systems. The main purpose is to obtain delay-dependent stability conditions that can be imposed by means of an appropriate switching strategy. Both cases of switching strategies corresponding to state and output feedback are considered. The new version of SGT is specially important in the framework of switched linear systems because it allows robustness analysis with respect to parameter or frequency domain uncertainty arising in ℋ∞ control problems and constant time-delay modeling. Since only sufficient conditions are given, the conservativeness of the final results is evaluated in terms of the gain promoted by the switching strategy, exclusively. The theory is illustrated by means of academic examples.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
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    ABSTRACT: In this paper, we propose contributions on the stabilization and control of switched linear systems subject to time-delays through the assignment of the switching law. As a first step, based on previous results related to switched linear systems with no time-delays and exploiting the concept of piecewise quadratic Lyapunov–Krasovskii functionals, we solve the problem of finding suitable state-dependent switching laws ensuring the prescribed control objectives. Secondly, we extend such results and present a strategy to construct an output feedback switching law, based on the available measurements made on the system. In both cases, the design of the control strategy is done by computing a feasible solution to a set of matrix inequalities associated to the modes of the switched linear system. Copyright © 2011 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 07/2011; · 1.90 Impact Factor
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    ABSTRACT: This paper deals with discrete-time switched linear systems and considers the problem of computing an upper bound to the dwell time ensuring a pre-specified root mean square (RMS) gain. As a natural consequence of treating general systems of this class in terms of the order and the number of subsystems, only sufficient conditions are worked out. They depend on the complete separation of the stabilizing and anti-stabilizing solutions of the algebraic Riccati equation associated to each subsystem. Moreover, as positive features, it is shown that the dwell time preserving the specification can be calculated through linear matrix inequalities (LMIs) and line search, being thus numerically solvable in polynomial time, and this allows the treatment of stable switched linear systems which do not admit a common Lyapunov function. The case of a guaranteed RMS gain for arbitrary switching signals is also addressed. A simple academic example constituted by three subsystems of third order is included for illustration.
    Automatica. 01/2011; 47:1677-1684.
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    ABSTRACT: The problem considered in this paper is the study and the control strategy design of semi-active suspensions, featuring the regulation of both damping and stiffness. The first contribution of this paper is the introduction and the analysis of two architectures based on the use of only controllable dampers, which make possible the emulation of an ideal suspension with controllable-damping-and-stiffness. This work presents an evaluation of the performances and drawbacks achieved by such suspension architectures, also in a nonlinear setting (explicitly taking into account the stroke limits of the suspension). This paper then proposes a new comfort-oriented variable-damping-and-stiffness control algorithm, named stroke–speed–threshold–stiffness–control, which overcomes the critical trade-off between the choice of the stiffness coefficient and the end-stop hitting. The use of a variable-damping-and-stiffness suspension, together with this algorithm, provides a significant improvement of the comfort performances, if compared with traditional passive suspensions and with more classical variable-damping semi-active suspensions.
    Vehicle System Dynamics 01/2011; 49:237-256. · 0.77 Impact Factor
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    ABSTRACT: The stability of a class of Markov jump linear systems (MJLS) characterized by constant transition rates and piecewise-constant system dynamics is investigated. For these Switching Dynamics Markov jump linear systems (SD-MJLS), almost sure exponential stability (ASE-stability) is analyzed by applying the ergodic law of large numbers under the assumption that suitable average contractivity conditions are satisfied. The main result is a sufficient condition that guarantees ASE-stability under constraints on the dwell-time between switching instants.
    01/2011;
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    ABSTRACT: The problem of H filtering for time-invariant linear systems with sampled measurements is considered. Sufficient and neces ary conditions are derived that ensure the existence of a finite-horizon filter and the convergence of this filter to the infinite-horizon one. The convergence conditions are given in terms of allowable regions for the initial state error weighting matrix.
    International Journal of Control 11/2010; 73(15):1382-1391. · 1.01 Impact Factor
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    ABSTRACT: The problem considered in this paper is the study and the control strategy design of semi-active suspensions featuring the regulation of both damping and stiffness. This work presents an evaluation of the performances and drawbacks achieved by such suspension architecture, also in a non-linear setting (explicitly taking into account the stroke limits of the suspension). This paper then proposes a new comfort-oriented variable-damping-and-stiffness control algorithm, named Stroke-Speed-Threshold-Stiffness-Control (SSTSC), which overcomes the critical trade-off between the choice of the stiffness coefficient and the end-stop hitting. The use of a variable-damping-and-stiffness suspension, together with this algorithm, provides a significant improvement of the comfort performances, if compared with traditional passive suspensions and with more classical variable-damping semi-active suspensions.
    American Control Conference (ACC), 2010; 08/2010
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    ABSTRACT: This work deals with the robust almost sure (AS) stabilization problem for continuous-time Markov jump linear systems (MJLS). Norm-bounded uncertainties affecting the system state and input matrices are considered. A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix. Such a condition can be profitably employed also to design a robust feedback stabilization strategy. Such feedback design is based on a formulation of the sufficient condition for robust AS stability in terms of an equivalent LMI problem.
    IEEE Transactions on Automatic Control 02/2010; · 2.72 Impact Factor
  • J. C. Geromel, P. Colaneri, P. Bolzern
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    ABSTRACT: Passivity is one of the key concepts related to LTI systems. Passive systems are not only stable but they are intrinsically robustly stable with respect to a wide class of feedback disturbance. Passivity can be characterized either in time domain or in frequency domain from positive realness. This paper aims to generalize this concept to continuous-time switched linear systems. Analysis is performed by taking into account state dependent and arbitrary time dependent switching function with a prescribed dwell time. A control design problem related to the determination of a switching strategy, based upon output measurements, that renders a switched linear system passive is also considered. A simple example of passivation by means of a switching function illustrates the theoretical results.
    01/2010;
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    ABSTRACT: This article deals with the design and synthesis of limit cycles for a class of switched linear systems. This work is motivated by an application in the context of electrical networks, but the methodologies can be applied in other engineering fields as well. Several methods for the design and synthesis of limit cycles are presented. Based on a monodromy matrix associated with a periodically switched system, a design method and two feedback strategies are developed. The first strategy is based on linear feedback design using pole placement. The second strategy is based on the observation that certain state-dependent switching strategies can be implemented by means of a simple nonlinear output feedback controller. Advantages of this latter strategy are not only the ease with which the switching strategy can be implemented, but also the fact that classical techniques may also be used to ascertain the stability of the resulting limit cycle. Our next contribution is the development of a novel frequency domain-based approach to limit cycle design. This approach is based on the observation that the existence of certain limit cycles can be deduced from an infinity of circle criteria generated by a family of periodic systems. By making use of recent results, this observation can be used to develop a one-parameter spectral search to deduce the approximate frequencies of feasible limit cycles. Having selected a frequency of oscillation, one may then make use of the aforementioned nonlinear elements to realise a switching strategy that generates a stable limit cycle with given frequency and amplitude. Examples are given to illustrate the effectiveness of the approaches presented.
    International Journal of Control 01/2010; 83(5):915-927. · 1.01 Impact Factor
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    ABSTRACT: The stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics is investigated. For these Switching Markov Jump Linear Systems, mean square stability is analyzed through the time evolution of the second-order moment of the state. The main result is a sufficient condition that guarantees mean square stability under constraints on the dwell-time between switching instants. An alternative condition based on Kronecker calculus is worked out. It is shown that both the stability criteria admit an LMI implementation.
    Automatica 01/2010; 46:1081-1088. · 2.92 Impact Factor

Publication Stats

567 Citations
83.53 Total Impact Points

Institutions

  • 1985–2011
    • Politecnico di Milano
      • • Department of Electronics, Information, and Bioengineering
      • • Department of Electrical Engineering
      Milano, Lombardy, Italy
  • 2008
    • University of Campinas
      Conceição de Campinas, São Paulo, Brazil
  • 1995–2006
    • University of Pavia
      • Department of Electrical, Computer and Biomedical Engineering
      Ticinum, Lombardy, Italy
  • 2004
    • University of Milan
      Milano, Lombardy, Italy
  • 1990
    • Università Telematica "Leonardo da Vinci"
      Milano, Lombardy, Italy