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An extension of LaSalle’s Invariance Principle for a class of switched linear systems

Authors
Journal
Systems & Control Letters
0167-6911
Publisher
Elsevier
Publication Date
Volume
58
Identifiers
DOI: 10.1016/j.sysconle.2009.08.008
Keywords
  • Lasalle’S Invariance Principle
  • Switched Linear Systems
  • Weak Common Quadratic Lyapunov Function

Abstract

Abstract In this paper LaSalle’s Invariance Principle for switched linear systems is studied. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, in this paper the switching modes are allowed to be only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle’s Invariance Principle for global asymptotic stability of switched linear systems is proposed provided that the kernels of derivatives of a common quadratic Lyapunov function with respect to the switching modes are disjoint (except the origin).

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