Small-gain theorems of LaSalle type for hybrid systems

We study stability of hybrid systems described as feedback interconnections of smaller subsystems, within a Lyapunov-based ISS small-gain analysis framework. We focus on constructing a weak (nonstrictly decreasing) Lyapunov function for the overall hybrid system from weak ISS-Lyapunov functions for the subsystems in the interconnection. Asymptotic stability of the hybrid system is then concluded by applying results of LaSalle type. The utility of this approach is illustrated on feedback systems arising in event-triggered control and quantized control.