Expansions and contractions of hybrid systems

Inclusion and extension principles are defined and studied for hybrid systems. The controller design problem for hybrid systems is then considered within the framework of the extension principle. It is shown that if the extension principle is used then any controller designed in the expanded spaces is contractible to the original spaces for implementation. Stability of hybrid systems is also considered. It is shown that if a system, which includes another system is stable, then the included system is also stable. Furthermore, it is shown that, if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system.