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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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 61; no. 9; pp. 2512 - 2517
Main Authors: Fiacchini, Mirko, Morarescu, Irinel-Constantin
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2496792