Cyber-Resilient Reachable Set Control for Discrete-Time Delayed Markov Jump Systems Subject to Mismatched Modes

This paper addresses the issue of reachable set control for discrete-time delayed Markov jump systems (DTDMJSs) under cyber-attacks, with a focus on enhancing exponential-dependent estimation techniques within the Lyapunov-Krasovskii functional (LKF) framework. Firstly, considering the impact of stochastic Denial-of-Service (DoS)/deception attacks in complex network environments, a resilient mismatched controller is designed to establish the closed-loop Markov jump systems. To improve the estimation of summation terms involving exponentially dependent states, two refined free-matrix-based summation inequalities are established. Based on these improvements, less conservative criteria are derived to guarantee the existence of an ellipsoidal reachable set for DTDMJSs. Finally, two numerical examples are provided to demonstrate the effectiveness and improvements of the proposed approaches.