Event-Triggered and Self-Triggered $H_\infty$ Control of Uncertain Switched Linear Systems

Abstract

This paper studies the problem of event-triggered and self-triggered H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controls for uncertain switched linear systems with exogenous disturbances whose magnitude is bounded by the system state's norm. With the proposed schemes, the control task is carried out only when the triggering condition is met. That leads to changing and adaptive interexecution intervals and can further reduce the system resource costs to a certain extent. Moreover, to ensure the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control performance of the event-triggered switched system, a proof which makes certain that the occurrence of Zeno problem can be prevented is first provided. Then, by adopting the average dwell time method, a set of sufficient conditions for H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis is developed. Subsequently, the codesign of controller gains and event-triggering schemes is provided. On the basis of the eventtriggered control, a solution to the self-triggered control problem is then presented. It can only utilize the current sampled data to predict the next triggered instant. Finally, in order to test the effectiveness of the proposed methods, numerical simulations are performed.