On Event-Triggered Control for Singular Systems

This paper deals with the state feedback control of singular continuous-time linear systems with discrete-time measurement of the state. Intuitively, descriptor or singular description of linear systems is more general than conventional state space description. In particular, a descriptor form includes information about algebraic as well as dynamic constraints. The use of an event-triggering mechanism results in a varying sampling-time period. Moreover, it is worth noting that the system is really in open loop during the inter-event time interval. The consequence is that there is no means to make the system admissible and by the way all the nice theory of admissibilization becomes useless. Hence, a continuous-time singular system in a sampled data closed-loop framework is badly posed unless the open loop is regular. In the case the open-loop system is regular, it is shown that the fast component of the state vector exhibits a discontinuous behavior. The dynamic event-triggering mechanism is shown to insure that the inter-event time interval is lower bounded, and as a consequence, it avoids the Zeno phenomenon. Simulations are presented to illustrate the obtained results.