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A LIE ALGEBRAIC CONDITION OF STABILITY FOR HYBRID SYSTEMS AND APPLICATION TO HYBRID SYNCHRONIZATION

SHOUWEI ZHAO

Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

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and

JITAO SUN

Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

Author for correspondence.

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https://doi.org/10.1142/S0218127409022932Cited by:7 (Source: Crossref)

Abstract

In this paper, we first present a Lie algebraic condition for global exponential stability of linear switched and impulsive systems. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Hurwitz/Schur stable we derive a new criterion for global exponential stability of linear switched and impulsive systems. Then a simple sufficient condition in terms of Lie algebra is established for a nonlinear system synchronization using a hybrid switched and impulsive control. As an application, Chua's chaotic circuit's synchronization is investigated by our method while synchronization cannot be achieved with the existing result.

This work is supported by the NNSF of China under Grant 60874027.

Keywords:

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