Nonlinear integral control with event-triggered feedback: Unknown decay rates, zeno-freeness, and asymptotic convergence

Abstract

This paper studies the event-triggered implementation of integral control laws for nonlinear uncertain systems. It is assumed that the plant already admits an integral control law such that the closed-loop system is input-to-state stable (ISS) with respect to the state sampling errors and admits an ISS-Lyapunov function. The unknown offset between the plant equilibrium and the set point means that one may not find a uniform lower bound for all the possible decay rates of the ISS-Lyapunov function, which however is usually required in the existing results. The design in this paper is based on a sequence of lower bound estimates of the decay rate, and the proposed dynamic event trigger guarantees that the intersampling intervals are lower bounded by a positive constant, and the asymptotic convergence property of integral control is retained even with event-triggered feedback. The theoretical result is physically validated by a pendulum control system.