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

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.