Asynchronous event-triggered H∞ control for 2D Markov jump systems subject to networked random packet losses

This paper investigates the issue of asynchronous event-triggered control for two-dimensional Markov jump systems subject to networked random packet losses. The asynchronous behavior between the plant and controller is characterized by a hidden Markov model, and the packet loss behavior is described by a Bernoulli stochastic process. To relieve the communication pressure, an event-triggered strategy with independent triggering behavior in the horizontal and vertical directions is given. A sufficient condition is established to ensure stochastic stability and H∞ performance for the closed-loop system. Then, a method for designing an asynchronous event-triggered controller is developed through eliminating nonlinearities formed by the inverse of Lyapunov matrices. Moreover, based on convex optimization of the H∞ performance, an algorithm is proposed to find the maximum feasible domain of the event-triggered thresholds. Finally, a Darboux equation with Markov jump properties is applied to verify the effectiveness of the presented design method. •Compared with existing studies on event-triggered H∞ control for 2D Markov jump systems, the present work allows for random packet losses and, therefore, enhances the robustness of the control framework.•An asynchronous event-triggered controller is designed to ensure that the closed-loop system is stochastically stable with an H∞ performance.•Based on the convex optimization of H∞ performance, an algorithm is given to find the maximum feasible domain of the event-triggered thresholds.•In the absence of packet losses, the proposed controller design method numerically exhibits lower conservativeness than a recently reported method.