A note on multiple lyapunov functions and stability condition for switched and hybrid systems

Guisheng Zhai; Isatada Matsune; Joe Imae; Tomoaki Kobayashi

A note on multiple lyapunov functions and stability condition for switched and hybrid systems

Guisheng Zhai, Isatada Matsune, Joe Imae, Tomoaki Kobayashi

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, we consider stability condition with multiple Lyapunov functions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation interval of each subsystem, we propose a new Lyapunov stability condition, which complements the existing stability conditions that evaluate the value of multiple Lyapunov functions at the starting points or the ending points. We present several demonstrative examples, including the case where unstable subsystems are involved, and also apply the stability condition and the switching strategy to the switching control problem for stabilization of nonholonomic systems.

Original language	English
Pages (from-to)	1189-1199
Number of pages	11
Journal	International Journal of Innovative Computing, Information and Control
Volume	5
Issue number	5
Publication status	Published - 2009 May
Externally published	Yes

Keywords

Average value of multiple lyapunov functions
Lyapunov stability
Multiple Lyapunov functions
Nonholonomic systems
Switched and hybrid systems
Switching strategy

ASJC Scopus subject areas

Software
Theoretical Computer Science
Information Systems
Computational Theory and Mathematics

Cite this

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AB - In this note, we consider stability condition with multiple Lyapunov functions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation interval of each subsystem, we propose a new Lyapunov stability condition, which complements the existing stability conditions that evaluate the value of multiple Lyapunov functions at the starting points or the ending points. We present several demonstrative examples, including the case where unstable subsystems are involved, and also apply the stability condition and the switching strategy to the switching control problem for stabilization of nonholonomic systems.

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KW - Lyapunov stability

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A note on multiple lyapunov functions and stability condition for switched and hybrid systems

Abstract

Keywords

ASJC Scopus subject areas

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