Event-Separation Properties and Asymptotic Behaviour of Hybrid Event-Based Control Systems

In hybrid event-based control (HEBC) systems the controller influences a continuous plant $G$ through two input signals with different characteristics. A continuous input is used to attenuate disturbances and to force the plant to follow a reference signal, whereas a discrete-valued input is determined by an event-based component of the controller in order to adjust the operation point of the plant. HEBC systems have typical characteristics of hybrid dynamical systems including state jumps and switching dynamics. This paper analyses HEBC systems with linear components. It derives bounds on the event threshold in order to avoid Zeno behaviour and to guarantee a minimum inter-event time. The main result is a condition under which the closed-loop system is asymptotically stable and has an asymptotic set-point tracking behaviour. An application example illustrates the results.