ℒ2 gain analysis of switched symmetric systems with time delays

Anthony N. Michel; Guisheng Zhai; Xinkai Chen; Ye Sun

ℒ₂ gain analysis of switched symmetric systems with time delays

Anthony N. Michel, Guisheng Zhai, Xinkai Chen, Ye Sun

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

Abstract

In this paper, we study ℒ₂ gain property for a class of switched systems which are composed of a finite number of linear time-invariant (LTI) symmetric subsystems with time delays in system states. We show that when all subsystems have ℒ₂ gain γ in the sense of satisfying an LMI, the switched system has the same ℒ₂ gain γ under arbitrary switching. The key idea is to establish a common Lyapunov function for all subsystems in the sense of ℒ₂ gain.

Original language	English
Pages (from-to)	219-232
Number of pages	14
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume	11
Issue number	2-3
Publication status	Published - 2004 Apr 1
Externally published	Yes

Keywords

Arbitrary switching
Common Lyapunov function
Linear matrix inequality (LMI)
Switched symmetric system
Time delay
ℒ gain

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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AB - In this paper, we study ℒ2 gain property for a class of switched systems which are composed of a finite number of linear time-invariant (LTI) symmetric subsystems with time delays in system states. We show that when all subsystems have ℒ2 gain γ in the sense of satisfying an LMI, the switched system has the same ℒ2 gain γ under arbitrary switching. The key idea is to establish a common Lyapunov function for all subsystems in the sense of ℒ2 gain.

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KW - Linear matrix inequality (LMI)

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ℒ₂ gain analysis of switched symmetric systems with time delays

Abstract

Keywords

ASJC Scopus subject areas

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