ℒ2 gain analysis for switched symmetric systems with time delay under arbitrary switching

In this paper, we study L₂ gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric systems with time delay. We show that when all subsystems have the L₂ gains 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.