Input-to-state stability of integral-based event-triggered control for linear plants

Integral-based event-triggered control utilizes the integrals of system states to construct the event conditions. By this means, the integral-based event-triggered control can relax the requirements on the derivative of the Lyapunov function, and then, may yield better sampling performance. In this paper, the effects of bounded disturbances on the integral-based event-triggered control systems are studied. Results on input-to-state stability with respect to the external disturbances are presented for linear plants with observer-based output feedbacks. An estimation on the upper bound of the input-to-state stability gain is given analytically. Then it is shown that for integral-based event-triggered control, a pre-specified upper bound of inter-event times is necessary to ensure the input-to-state stability. Furthermore, it is proved that increasing the pre-specified upper bound can only enlarge the input-to-state stability gain but cannot destroy the input-to-state stability. Moreover, a positive lower bound of inter-event times is provided to exclude Zeno behaviors. Finally, numerical examples are given to illustrate the efficiency and the feasibility of the proposed results.