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Observer-based finite-time controller for Markov jump systems with deterministic switches

The observer-based controller with finite-time bounded property design technique for a class of discrete-time Markov jump linear systems governed by deterministic switches is presented in this paper. Less conservative conditions are derived to ensure the state trajectories of the closed-loop systems keep within the desired bound in given-time interval by allowing the Lyapunov function to increase at every switching instant with a limited increasing rate. Meanwhile, considering the effect of time-delay on the transient performance of the systems, the analytic form of the relationship among time-delay, average dwell time and given finite time horizon are obtained through an average dwell time constraint. A numeric example is given to verify the results we derived.