Paolo Bolzern

Politecnico di Milano, Milano, Lombardy, Italy

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Publications (105)106.83 Total impact

  • P. Bolzern · P. Colaneri · G. De Nicolao
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    ABSTRACT: It is known that the discrete-time H∞ finite-horizon filter exists provided that the solution of a suitable H∞ Difference Riccati Equation (DRE) exists and satisfies a "feasibility" condition. In the paper, sufficient conditions ensuring feasibility and convergence to the steady-state stabilizing solution are derived. In particular, convergence can be guaranteed if the initial condition of the DRE is not much greater than the stabilizing solution. For a fixed value of the attenuation level γ, the finite-horizon H∞filter may fail to converge to the steady-state stabilizing filter. Hence, a strategy employing a time varying attenuation level γ(t) is worked out so as to ensure both feasibility and convergence to the desired steady-state filter.
    No preview · Article · Apr 2015
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    ABSTRACT: The problem considered in this paper is the design and analysis of implementable architectures for semi-active suspensions characterized by a regulation of both damping and stiffness coefficients. The first contribution of this paper is the introduction of a suspension architecture that makes possible the emulation of the behavior of an ideal suspension with variable spring by using only shock absorbers. Taking into account the comfort objective, a full analysis on the advantages and drawbacks of this kind of suspension is provided. This paper proposes a very simple novel comfort-oriented stiffness-damping control algorithm to highlight the benefits provided by this system.
    No preview · Article · Mar 2015
  • P. Bolzern · P. Colaneri · G. De Nicolao
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    ABSTRACT: This paper deals with the stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics. These systems are called Switching Markov Jump Linear Systems. Mean square stability analysis is carried out by studying the time evolution of the second-order moment of the state. A sufficient condition guaranteeing mean square stability under constraints on the dwell-time between switching instants is derived. It is shown that such a condition, as well as another one based on Kronecker calculus, admit an LMI implementation.
    No preview · Article · Mar 2015
  • I. Boniolo · P. Bolzern · P. Colaneri · M. Corless · R. Shorten
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    ABSTRACT: This paper deals with the stability of limit cycles for a class of linear switching systems. Such applications arise in the context of electrical networks. An autonomous RLC circuit with switching capacitor is considered. A two-step method is given to design limit cycles for this application. First we give a proedure for determining the feasible approximate frequencies at which limit cycles may exist. Then, we give a method to design nonlinear controllers to achieve a stable limit cycles at a given frequency. An example is given to illustrate the methods.
    No preview · Article · Mar 2015
  • P. Bolzern · P. Colaneri · G. De Nicolao
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    ABSTRACT: This paper deals with positive Markov jump linear systems with an additional switching control signal that affects the stochastic subsystems dynamics. This control signal is used for stochastic stabilization and performance optimization. Stability for MJLS is considered in the sense of mean stability and almost-sure stability. Various sufficient conditions for stabilization and performance optimization are worked out, exploiting the positiveness of the system and the concept of stochastic co-positive piecewise linear control Lyapunov function.
    No preview · Article · Feb 2015 · Proceedings of the IEEE Conference on Decision and Control
  • Paolo Bolzern · Patrizio Colaneri

    No preview · Article · Jan 2015
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    ABSTRACT: This paper addresses the probabilistic consensus problem in a network of Markovian agents. The dynamics of each agent ismodeled as a finite-state Markov chain, with transition rates that are affected by the communication with the neighbors, so inducing an emulation effect. Consensus is reached when all the agent probability vectors converge to a common steady-state probability vector. The main result of the paper is the proof of consensus for communication networks described by either a complete graph or a star-topology graph. These results are also important in a network control perspective, as some parameters of the network model could be used as tuning knobs to steer the steady-state consensus wherever desired.
    No preview · Conference Paper · Jun 2014
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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.
    No preview · Article · Apr 2014 · Automatica
  • P. Bolzern · P. Colaneri · G. De Nicolao
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    ABSTRACT: Dual switching linear systems are systems with piecewise linear dynamics governed by two distinct external switching signals. In this paper one switching signal is stochastic and modeled as a time-homogeneous Markov chain, and the second one is assumed to be a control signal taking values in a finite set. This situation arises, for instance, in multi-loop networked control systems (NCS) with limited transmission capacity and lossy communication channels, where the control variable is the scheduling signal and the stochastic switching accounts for packet dropout. The aim of this paper is to derive suitable switching strategies for dual switching linear systems, ensuring mean-square stability and attaining guaranteed bounds on H2 and H∞ performance indices. The relevant sufficient conditions are expressed in terms of feasibility of sets of coupled matrix inequalities. The application to a scheduling design problem in NCS's is also discussed.
    No preview · Article · Jan 2014
  • Paolo Bolzern · Grace S. Deaecto · Luca Galbusera
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    ABSTRACT: This paper investigates the problem of designing suitable switching strategies for stabilizing a switched linear system subject to a time-varying delay, assumed to lie in a bounded interval. Based on an extended version of the small gain theorem, two distinct globally stabilizing switching laws expressed in a state-feedback form are worked out. The first one requires the knowledge of an upper bound on the time-variation rate of the delay, while the second one does not rely on this information and it applies also when the time variation rate is greater than 1, which is known to be a very demanding situation. Both switching strategies are then extended to cope with the case when only a measured output vector is available for feedback. All conditions are formulated in terms of Lyapunov-Metzler inequalities, which allow maximization of the upper bound on the delay for which stability is guaranteed. A simple numerical example is provided to show the effectiveness of the proposed approach.
    No preview · Conference Paper · Dec 2013
  • Source
    Ali H. Sayed · P. Bolzern · P. Colaneri · G. De Nicolao

    Preview · Article · Jul 2013 · European Journal of Control
  • Source
    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.
    Preview · Article · Jul 2013 · European Journal of Control
  • 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.
    No preview · Article · Jul 2013 · International Journal of Control
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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.
    No preview · Article · Jun 2013 · International Journal of Control
  • 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.
    No preview · Conference Paper · Jan 2013
  • 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.
    No preview · Conference Paper · Jan 2013
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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.
    No preview · Article · Jan 2013 · IEEE Transactions on Automatic Control
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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.
    No preview · Conference Paper · Dec 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.
    Preview · Article · Oct 2012 · International Journal of Robust and Nonlinear Control
  • José C. Geromel · Patrizio Colaneri · Paolo Bolzern
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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.
    No preview · Article · Apr 2012 · Systems & Control Letters

Publication Stats

1k Citations
106.83 Total Impact Points

Institutions

  • 1985-2014
    • Politecnico di Milano
      • Department of Electronics, Information, and Bioengineering
      Milano, Lombardy, Italy
  • 2004
    • University of Milan
      Milano, Lombardy, Italy
  • 1990
    • Università Telematica "Leonardo da Vinci"
      Milano, Lombardy, Italy
  • 1988
    • INO - Istituto Nazionale di Ottica
      Florens, Tuscany, Italy