Resilient dynamic output feedback control for discrete-time descriptor switching Markov jump systems and its applications

Abstract

This paper investigates the resilient dynamic output feedback (DOF) control problem for discrete-time descriptor switching Markov jump systems for the first time, where the time-varying transition probabilities are described by a piecewise-constant matrix and a high-level signal subject to average dwell time switching. The controllers to be designed can tolerate additive gain perturbations. Firstly, by constructing a stochastic Lyapunov functional and using an average dwell time method, a sufficient condition is given such that the resultant closed-loop systems are stochastically admissible and have a $$H_{\infty }$$ noise attenuation performance. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented such that the resultant closed-loop systems are stochastically admissible with a $$H_{\infty }$$ noise attenuation performance. When the uncertain parameters exist not only in plant matrices but also in controller gain matrices, the resilient DOF controller is developed in terms of LMIs, which can be of full order or reduced order. Compared with the previous ones, the proposed design methods do not impose extra constraints on system matrices or slack variables, which show less conservatism. Finally, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.