Stability and £2 Gain Analysis of Switched Symmetric Systems
We study stability and £2 gain properties for a class of switched systems that are composed of a finite number of linear time-invariant symmetric subsystems. We consider both continuous-time and discrete-time switched systems. We show that when all the subsystems are (Hurwitz or Schur) stable, the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all the subsystems have £2 gain less than a positive scalar γ,the switched system has £2 gain less than the same γ under arbitrary switching. We also extend the results to switched symmetric systems with time delay in system state for continuous-time switched systems. The key idea for both stability and £2 gain analysis in this chapter is to establish a common Lyapunov function for all the subsystems in the switched system.
KeywordsAttenuation DiCi Subsys
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