Robust $H_{\infty}$ Control of Markov Jump Systems with Time-Delay and Actuator Saturation

To address the issue of conserving network resources, our study focuses on the challenge of implementing optimal state feedback control for Markov Jump systems. These systems present complexities associated with input saturation and time delays. Unlike the traditional static approach, we introduce a dynamic event-triggered mechanism that extends the interval between two consecutive occurrences beyond conventional methods. Firstly, we establish sufficient conditions for the stochastic stability of controlled Markov Jump systems (MJS) by utilizing the proposed dynamic event-triggered mechanism and Linear Matrix Inequalities (LMIs). Then, based on the obtained results, controllers are designed to ensure the asymptotic stability of the considered closed-loop system. Furthermore, in order to determine the maximum estimate of the domain of attraction (DOA), an optimization approach has been employed. Our approach is exemplified through notable instances, demonstrating how the suggested dynamic event-triggered mechanism (DETM) performs comparably while achieving better resource conservation compared to the static event-triggered mechanism (ETM).