Practical stability of integral-based event-triggered control systems

This paper studies the practical stabilization of nonlinear event-triggered control systems in the presence of bounded disturbance. An integral-based triggering condition is employed to generate the events. The event is triggered when the integral of the absolute measurement error, between the latest sampled and the current states, violates a time-varying threshold. It is proved that the closed-loop nonlinear system is practically stable, i.e., the state of the system is bounded with a bound depending on the initial state, the bound of the disturbances, and the parameters in the triggering conditions. Then, a positive estimate of minimum inter-event time is provided to exclude the Zeno behaviors. Moreover, for the integral-based event-triggered control, it is shown that a pre-specified upper bound of inter-event times is necessary to ensure the practical stability. Finally, a numerical example is provided to illustrate the efficiency and the feasibility of the obtained results.