A unified approach to analysis of switched linear descriptor systems under arbitrary switching

We establish a unified approach to stability and L
₂
gain analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain L
₂
gain of all subsystems, then the switched system is stable and has the same L
₂
gain under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.