Event-triggered robust H ∞ control for linear systems with disturbance

Event-triggered control has received considerable attention for the benefits it brought, like reducing the resource utilization (e.g.,communication load and processor), and providing more system robustness. However, it requires persistent information of the system states to determine at which time the control input should be updated and transmitted to the plant. Self-triggered scheme was then proposed to eliminate this disadvantage, but also sacrifice the system robustness. In this paper, we introduce robust H ∞ theory into self-triggered sample strategy, and achieve both resource utilization and disturbance attenuation properties at the same time. Firstly, we investigate the full-information feedback H ∞ control for the perturbed linear system in a very general form, a sufficient condition guaranteeing the asymptotic stability and robustness of the system is given in the form of LMI(Linear Matrix Inequality). And the event condition is proposed based on the relative error between the current state and the state at last sample time. We also exploit a corresponding self-triggered control system and give a method of designing the longest sampling period for the relevant H ∞ controller on the premise that the system is stabilized and robust. Illustrative example is given to show the efficiency of the theoretical result.