Stability analysis and design of switched normal systems

In this paper, we study stability property for a class of switched systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time. When all continuous-time subsystems are Hurwitz stable and all discrete-time subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for the subsystems and that the switched system is exponentially stable under arbitrary switching. When unstable subsystems are involved, we show that given a desired decay rate of the system, if the activation time ratio between unstable subsystems and stable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.