Markov Switching Topology-Based Reliable Control Design for Delayed Discrete-Time System: An Ellipsoidal Attracting Approach

This article presents reachable set synthesis for a discrete-time Markov jump system (DTMJS) with mode-dependent time-varying delays, subjected to uncertain transition probabilities and actuator faults, based on the ellipsoidal attracting approach. The focus is mainly to reflect more realistic control behaviors for the proposed DTMJS, in which the class of partially asynchronous reliable control (PARC) scheme is designed for the first time under the Markov switching topology. In this regard, the state-feedback and mode-dependent time-varying delayed state-feedback controllers are coupled by employing the Bernoulli variable. Under this framework, the hidden Markov model is formulated, revealing the asynchronism among switching topology, controller, actuators and proposed system in different operational modes. By constructing a double mode-dependent stochastic Lyapunov-Krasovskii functional, the sufficient conditions are derived in terms of linear matrix inequalities, which not only ascertain the stochastic stability of the resultant Markov jump system but also ensure that all reachable states remain within compact ellipsoidal boundaries. Finally, numerical simulations are provided to verify the effectiveness and merits of the presented method.