Constructive Necessary and Sufficient Condition for the Stability of Quasi-Periodic Linear Impulsive Systems

The technical note provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, th...

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Vydané v:IEEE transactions on automatic control Ročník 61; číslo 9; s. 2512 - 2517
Hlavní autori: Fiacchini, Mirko, Morarescu, Irinel-Constantin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.09.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Predmet:
Algorithms
Approximation methods
Automatic Control Engineering
Computation
Computer Science
Construction methods
Linear systems
Lyapunov functions
Lyapunov methods
Numerical stability
Reset systems
set theory
Stability
Stability analysis
Test procedures
Uncertain systems
Yttrium
stability analysis
Reset systems
set theory
ISSN:0018-9286, 1558-2523
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Abstract The technical note provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing set-induced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set.
AbstractList The paper provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing set-induced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set.
The technical note provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing set-induced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set.
Author Fiacchini, Mirko
Morarescu, Irinel-Constantin
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  givenname: Irinel-Constantin
  surname: Morarescu
  fullname: Morarescu, Irinel-Constantin
  email: constantin.morarescu@univ-lorraine.fr
  organization: CRAN, Univ. de Lorraine, Vandœuvre-lès-Nancy, France
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Snippet The technical note provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose...
The paper provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions...
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SubjectTerms Algorithms
Approximation methods
Automatic Control Engineering
Computation
Computer Science
Construction methods
Linear systems
Lyapunov functions
Lyapunov methods
Numerical stability
Reset systems
set theory
Stability
Stability analysis
Test procedures
Uncertain systems
Yttrium
Title Constructive Necessary and Sufficient Condition for the Stability of Quasi-Periodic Linear Impulsive Systems
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