Robust H ∞ Triggered Control of Linear Systems

Abstract

In this paper, we study the impact of triggered control strategies for a class of uncertain linear systems. The event condition is proposed based on the relative error between the current state and the state at last sample time. We introduce robust H ∞ theory into self-triggered sample strategy, and achieve both resource utilization and disturbance attenuation properties. We investigate the full-information feedback H ∞ control for the perturbed linear system and develop a linear matrix inequality (LMI)-based sufficient condition guaranteeing the robust asymptotic stability of the closed-loop system. Employing a self-triggered control, we provide a method of designing the longest sampling period for the relevant H ∞ controller when the system is stabilized and robust. A cart and pendulum example is given to show the efficiency of the theoretical result.