Hybrid systems: solutions, stability, control

Abstract

This papers investigates the stability and control of hybrid systems. While stability is well defined and studied for continuous systems, hybrid systems (mixed continuous discrete systems) pose interesting and challenging new problems. The same holds for the question of control. We model hybrid systems using hybrid automata. The notion of observability and controllability is extended to hybrid system. We present a hybrid system adapted notion of stability including equilibrium and orbital stability, and show some implications. We discusses and define problems which arise in controlling hybrid systems, such as mode controllability.