G. Zhai, X. Chen (Japan), Y. Sun, and A.N. Michel (USA)
Switched symmetric system, time delay, asymptotic stability, L2 gain, arbitrary switching,common Lyapunov function, linear matrix inequality (LMI)
In this paper, we study stability and L2 gain properties for a class of switched systems com posed of a finite number of linear time-invariant symmetric time delay systems. We show that when all subsystems are asymptotically stable in the sense of satisfying an LMI, the switched system is also asymptotically stable under arbitrary switching. Furthermore, we show that when all subsystems are asymptotically stable and achieve the L2 gain γ in the sense of satisfying an LMI, the switched system is also asymptotically stable and achieves the L2 gain γ under arbitrary switching. The key idea for both stability and L2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.
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