The main contribution of this paper is a number of structure dependent stability results applicable to a class of hybrid systems modelled by discrete automata. Our main results are formulated as two stability theorems giving necessary and sufficient conditions for global stability of synchronous and asynchronous piecewise linear hybrid systems. These theorems effectively reduce the hybrid systems stability analysis problem to analysis of stability of a certain class of linear time varying systems.
37th IEEE Conference on Decision and Control. Proceedings of the 37th Conference on Decision and Control (Tampa, FL 1998) p. 3687-3692