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Mirko Fiacchini - One of the best experts on this subject based on the ideXlab platform.
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Dead-beat Stabilizability of discrete-time switched linear systems: algorithms and applications
IEEE Transactions on Automatic Control, 2019Co-Authors: Mirko Fiacchini, Gilles MillériouxAbstract:This paper deals with dead-beat Stabilizability of autonomous discrete-time switched linear systems. Based on a constructive necessary and sufficient condition for dead-beat Stabilizability, we propose two algorithms. The first one is concerned with the problem of testing dead-beat Stabilizability and computing the shorter stabilizing mode sequence, whenever it exists. The other one implements a method to construct a switched system whose shorter dead-beat stabilizing sequence has a prescribed length. Then, we present numerical assessments and possible applications.
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Stabilization and control Lyapunov functions for language constrained discrete-time switched linear systems
Automatica, 2018Co-Authors: Mirko Fiacchini, Marc Jungers, Antoine GirardAbstract:In this paper, the Stabilizability of discrete-time switched linear systems subject to constraints on the switching law is considered. The admissible switching sequences are given by the language generated by a nondeterministic finite state automaton. Constructive necessary and sufficient conditions for recurrent Stabilizability are given and the exact relations with the existence of control Lyapunov functions and with general Stabilizability are provided. The dependence of Stabilizability on the automaton initial state is also proved.
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Stabilizability and control co-design for discrete-time switched linear systems
2018Co-Authors: Mirko Fiacchini, Marc Jungers, Antoine Girard, Sophie TarbouriechAbstract:In this work we deal with the Stabilizability property for discrete-time switched linear systems. First we provide a constructive necessary and sufficient condition for Stabilizability based on set-theory and the characterization of a universal class of Lyapunov functions. Such a geometric condition is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for Stabilizability, derived from the geometric ones, are presented that permit to combine generality with convexity. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabiliz-ability conditions are analyzed to infer and compare their conservatism and their complexity. The results are finally extended to the problem of the co-design of a control policy, composed by both the state feedback and the switching control law, for discrete-time switched linear systems. Constructive conditions are given in form of LMI that are necessary and sufficient for the Stabilizability of systems which are periodic stabilizable.
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Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach
2016Co-Authors: Marc Jungers, Antoine Girard, Mirko FiacchiniAbstract:This paper addresses the issue of Stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite state automaton. Firstly the automaton is decomposed into strongly connected components to reduce the problem to the Stabilizability of each non trivial strongly connected component. Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed. Links with the current literature are discussed and a detailed example is given to illustrate our contributions.
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On the Stabilizability of discrete-time switched linear systems: novel conditions and comparisons
IEEE Transactions on Automatic Control, 2016Co-Authors: Mirko Fiacchini, Antoine Girard, Marc JungersAbstract:In this paper we deal with the Stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of Stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for Stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the Stabilizability conditions are analyzed to infer and compare their conservatism and their complexity.
Marc Jungers - One of the best experts on this subject based on the ideXlab platform.
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Stabilization and control Lyapunov functions for language constrained discrete-time switched linear systems
Automatica, 2018Co-Authors: Mirko Fiacchini, Marc Jungers, Antoine GirardAbstract:In this paper, the Stabilizability of discrete-time switched linear systems subject to constraints on the switching law is considered. The admissible switching sequences are given by the language generated by a nondeterministic finite state automaton. Constructive necessary and sufficient conditions for recurrent Stabilizability are given and the exact relations with the existence of control Lyapunov functions and with general Stabilizability are provided. The dependence of Stabilizability on the automaton initial state is also proved.
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Stabilizability and control co-design for discrete-time switched linear systems
2018Co-Authors: Mirko Fiacchini, Marc Jungers, Antoine Girard, Sophie TarbouriechAbstract:In this work we deal with the Stabilizability property for discrete-time switched linear systems. First we provide a constructive necessary and sufficient condition for Stabilizability based on set-theory and the characterization of a universal class of Lyapunov functions. Such a geometric condition is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for Stabilizability, derived from the geometric ones, are presented that permit to combine generality with convexity. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabiliz-ability conditions are analyzed to infer and compare their conservatism and their complexity. The results are finally extended to the problem of the co-design of a control policy, composed by both the state feedback and the switching control law, for discrete-time switched linear systems. Constructive conditions are given in form of LMI that are necessary and sufficient for the Stabilizability of systems which are periodic stabilizable.
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Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach
2016Co-Authors: Marc Jungers, Antoine Girard, Mirko FiacchiniAbstract:This paper addresses the issue of Stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite state automaton. Firstly the automaton is decomposed into strongly connected components to reduce the problem to the Stabilizability of each non trivial strongly connected component. Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed. Links with the current literature are discussed and a detailed example is given to illustrate our contributions.
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On the Stabilizability of discrete-time switched linear systems: novel conditions and comparisons
IEEE Transactions on Automatic Control, 2016Co-Authors: Mirko Fiacchini, Antoine Girard, Marc JungersAbstract:In this paper we deal with the Stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of Stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for Stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the Stabilizability conditions are analyzed to infer and compare their conservatism and their complexity.
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CDC - Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach
2016 IEEE 55th Conference on Decision and Control (CDC), 2016Co-Authors: Marc Jungers, Antoine Girard, Mirko FiacchiniAbstract:This paper addresses the issue of Stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite state automaton. Firstly the automaton is decomposed into strongly connected components to reduce the problem to the Stabilizability of each non trivial strongly connected component. Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed. Links with the current literature are discussed and a detailed example is given to illustrate our contributions.
Antoine Girard - One of the best experts on this subject based on the ideXlab platform.
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Stability and Stabilizability of discrete-time dual switching systems with application to sampled-data systems
Automatica, 2019Co-Authors: Lucien Etienne, Antoine Girard, Luca GrecoAbstract:In this paper, stability and Stabilizability of discrete-time dual switching linear systems is investigated. The switched systems under consideration have two switching variables. One of them is stochastic, described by an underlying Markov chain; the other one can be regarded either as a deterministic disturbance or as a control input, leading to stability or Stabilizability problems, respectively. For the considered class of systems, sufficient conditions for mean square stability (with or without control gain synthesis) and mean square Stabilizability are provided in terms of matrix inequalities. When the stochastic switching is driven by an independent identically distributed sequence, we establish simpler conditions without additional conservatism. Then, it is shown how the proposed framework can be used to study aperiodic sampled-data systems with stochastic computation times. The results are illustrated on examples borrowed from the literature.
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Stabilization and control Lyapunov functions for language constrained discrete-time switched linear systems
Automatica, 2018Co-Authors: Mirko Fiacchini, Marc Jungers, Antoine GirardAbstract:In this paper, the Stabilizability of discrete-time switched linear systems subject to constraints on the switching law is considered. The admissible switching sequences are given by the language generated by a nondeterministic finite state automaton. Constructive necessary and sufficient conditions for recurrent Stabilizability are given and the exact relations with the existence of control Lyapunov functions and with general Stabilizability are provided. The dependence of Stabilizability on the automaton initial state is also proved.
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Stabilizability and control co-design for discrete-time switched linear systems
2018Co-Authors: Mirko Fiacchini, Marc Jungers, Antoine Girard, Sophie TarbouriechAbstract:In this work we deal with the Stabilizability property for discrete-time switched linear systems. First we provide a constructive necessary and sufficient condition for Stabilizability based on set-theory and the characterization of a universal class of Lyapunov functions. Such a geometric condition is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for Stabilizability, derived from the geometric ones, are presented that permit to combine generality with convexity. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabiliz-ability conditions are analyzed to infer and compare their conservatism and their complexity. The results are finally extended to the problem of the co-design of a control policy, composed by both the state feedback and the switching control law, for discrete-time switched linear systems. Constructive conditions are given in form of LMI that are necessary and sufficient for the Stabilizability of systems which are periodic stabilizable.
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Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach
2016Co-Authors: Marc Jungers, Antoine Girard, Mirko FiacchiniAbstract:This paper addresses the issue of Stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite state automaton. Firstly the automaton is decomposed into strongly connected components to reduce the problem to the Stabilizability of each non trivial strongly connected component. Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed. Links with the current literature are discussed and a detailed example is given to illustrate our contributions.
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On the Stabilizability of discrete-time switched linear systems: novel conditions and comparisons
IEEE Transactions on Automatic Control, 2016Co-Authors: Mirko Fiacchini, Antoine Girard, Marc JungersAbstract:In this paper we deal with the Stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of Stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for Stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the Stabilizability conditions are analyzed to infer and compare their conservatism and their complexity.
Victor M. Preciado - One of the best experts on this subject based on the ideXlab platform.
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Resilient Structural Stabilizability of Undirected Networks
2019 American Control Conference (ACC), 2019Co-Authors: Jingqi Li, Ximing Chen, Sergio Pequito, George J. Pappas, Victor M. PreciadoAbstract:In this paper, we consider the structural Stabilizability problem of undirected networks. More specifically, we are tasked to infer the Stabilizability of an undirected network from its underlying topology, where the undirected networks are modeled as continuous-time linear time-invariant (LTI) systems involving symmetric state matrices. Firstly, we derive a graph-theoretic necessary and sufficient condition for structural Stabilizability of undirected networks. Then, we propose a method to determine the maximum dimension of the stabilizable subspace solely based on the network structure. Based on these results, on one hand, we study the optimal actuator-disabling attack problem, i.e., removing a limited number of actuators to minimize the maximum dimension of the stabilizable subspace. We show this problem is NP-hard. On the other hand, we study the optimal recovery problem with respect to the same kind of attacks, i.e., adding a limited number of new actuators such that the maximum dimension of the stabilizable subspace is maximized. We prove the optimal recovery problem is also NP-hard, and we develop a (1-1/e) approximation algorithm to this problem.
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ACC - Resilient Structural Stabilizability of Undirected Networks
2019 American Control Conference (ACC), 2019Co-Authors: Jingqi Li, Ximing Chen, Sergio Pequito, George J. Pappas, Victor M. PreciadoAbstract:In this paper, we consider the structural Stabilizability problem of undirected networks. More specifically, we are tasked to infer the Stabilizability of an undirected network from its underlying topology, where the undirected networks are modeled as continuous-time linear time-invariant (LTI) systems involving symmetric state matrices. Firstly, we derive a graph-theoretic necessary and sufficient condition for structural Stabilizability of undirected networks. Then, we propose a method to determine the maximum dimension of the stabilizable subspace solely based on the network structure. Based on these results, on one hand, we study the optimal actuator-disabling attack problem, i.e., removing a limited number of actuators to minimize the maximum dimension of the stabilizable subspace. We show this problem is NP-hard. On the other hand, we study the optimal recovery problem with respect to the same kind of attacks, i.e., adding a limited number of new actuators such that the maximum dimension of the stabilizable subspace is maximized. We prove the optimal recovery problem is also NP-hard, and we develop a $(1-1/e)$ approximation algorithm to this problem.
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Resilient Structural Stabilizability of Undirected Networks
arXiv: Optimization and Control, 2018Co-Authors: Jingqi Li, Ximing Chen, Sergio Pequito, George J. Pappas, Victor M. PreciadoAbstract:In this paper, we consider the structural Stabilizability problem of undirected networks. More specifically, we are tasked to infer the Stabilizability of an undirected network from its underlying topology, where the undirected networks are modeled as continuous-time linear time-invariant (LTI) systems involving symmetric state matrices. Firstly, we derive a graph-theoretic necessary and sufficient condition for structural Stabilizability of undirected networks. Then, we propose a method to infer the maximum dimension of stabilizable subspace solely based on the network structure. Based on these results, on one hand, we study the optimal actuator-disabling attack problem, i.e., removing a limited number of actuators to minimize the maximum dimension of stabilizable subspace. We show this problem is NP-hard. On the other hand, we study the optimal recovery problem with respect to the same kind of attacks, i.e., adding a limited number of new actuators such that the maximum dimension of stabilizable subspace is maximized. We prove the optimal recovery problem is also NP-hard, and we develop a (1-1/e) approximation algorithm to this problem.
Panos J Antsaklis - One of the best experts on this subject based on the ideXlab platform.
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stability and Stabilizability of switched linear systems a survey of recent results
IEEE Transactions on Automatic Control, 2009Co-Authors: Hai Lin, Panos J AntsaklisAbstract:During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching Stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching Stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic Stabilizability of switched linear systems is described here.
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switching Stabilizability for continuous time uncertain switched linear systems
IEEE Transactions on Automatic Control, 2007Co-Authors: Hai Lin, Panos J AntsaklisAbstract:This paper investigates the switching Stabilizability problem for a class of continuous-time switched linear systems with time-variant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic Stabilizability of such uncertain switched linear system is derived, under the assumption that the closed-loop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic Stabilizability of such continuous-time uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only
