On Detectability of a Class of Hybrid Systems

In this article, we model a hybrid system by using a hybrid machine consisting of an automaton and a set of continuous-variable subsystems. We investigate the problem of determining the (current) discrete state of the hybrid system. Extending the terminologies in discrete-event systems, a hybrid system is detectable if its discrete state can be uniquely determined. We derive conditions for a hybrid system to be detectable. If a hybrid system is detectable, we determine its current discrete state using a two-level approach. At the discrete-event level, we construct a discrete-event observer to obtain a discrete state estimate that consists of all possible discrete states that the hybrid system may be in. At the continuous-variable level, a set of continuous-variable observers are constructed, if necessary, to uniquely determine the discrete state. An example of a dc microgrid is used to illustrate the theoretical results.