Input-to-state practical stabilisation via periodic event-triggered control without Zeno-like behaviour

This paper studies periodic event-triggered control for systems with disturbances and output feedbacks. A new summation-based triggering condition is proposed to preserve the input-to-state practical stability for arbitrary positive parameters in the condition. Then, it is shown that the upper bound of the stability region, where the state eventually converges, depends on the parameters continuously. Furthermore, the ranges of the parameters, which lead to input-to-state stability, are given analytically. Moreover, the concept of Zeno-like behaviour is introduced, which characterises the phenomenon that the minimum inter-event times for periodic event-triggered control systems become arbitrarily small as the verification intervals of events go to zero. Then, the exclusion of Zeno-like behaviour for the designed event-triggered control systems is achieved. Finally, simulation examples are provided to illustrate the efficiency and feasibility of the obtained results.