Sliding Mode H∞ Control of Discrete-time Delayed Singular Markovian Jump Systems

This article addresses the problem of sliding mode control (SMC) for discrete-time delayed singular Markovian jump systems (MJSs) subject to parameter uncertainties and both of matched/mismatched disturbances. The transition probabilities of the Markov chain are considered to have partially unknown entries. Firstly, a sliding surface is proposed by taking the singular matrix into account, and hence the resultant dynamics of the sliding mode system becomes a full order delayed singular MJS. Secondly, the problem of bounded real lemma for the dynamics of the sliding mode system is investigated using the Lyapunov–Krasovskii functional. A delay-dependent solvability condition for the desired sliding surface is derived as linear matrix inequalities (LMIs), which guarantees that the dynamics of the sliding mode system to be robust stochastically admissible and satisfies the  performance. The slack matrix technique is utilized together with the delay partitioning approach to diminish the conservatism of the obtained condition. Thirdly, a sliding mode controller is synthesized to ensure that the sliding surface is reachable. Finally, two numerical examples are given to show the improved conservatism and the adequacy of the proposed design method.