Composite hierarchical anti‐disturbance control for discrete‐time singular Markov jump systems under double‐layer switching scheme

Abstract

This work endeavors to investigate the composite hierarchical anti-disturbance control issue for discrete-time singularly perturbed Markov jump systems with multiple disturbances. These disturbances include two types, one is the external disturbance that belongs to l 2 [0, ∞), and the other is generated by an exogenous system. To attenuate and reject the negative effects of two types of disturbances, a composite anti-interference controller with integrated feedforward and feedback strategies is designed. Notably, the transition probabilities of the Markov chain are considered to be piecewise time-varying and subject to a persistent dwell-time switching scheme. Fully considering the two-time scales phenomenon and the switching characteristics of systems, a mixed parameter/mode-dependent Lyapunov function is constructed to assure that all the signals of the closed-loop system satisfy the mean-square exponential stability with the anticipant  ∞ performance. Eventually, two illustrative examples are presented to verify the efficiency and superiority of the designed composite control strategy.