An inclusion principle for discrete-event and hybrid systems

Hybrid systems, which consist of continuous-state and discrete-state parts are considered. It is assumed that the discrete-state part of the system is event-driven. Inclusion and extension principles are first defined for such systems. The controller design problem for such 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, if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system. All the results may be specialized to the case of discrete-event dynamic systems.