This study considers the problem of finite-time H ∞ control for a class of discrete-time time-delay Markov jump linear systems governed by deterministic switches. By allowing the stochastic Lyapunov function to increase at every switching instant with a limited increase rate, new results on the stochastic finite-time boundness with given H ∞ disturbance attenuation level are derived. Moreover, the coupling relationship among time-delay, average dwell time and given finite-time horizon of the underlying system is obtained through an average dwell-time constraint. Finally, one example is given to demonstrate the validity of the obtained results.

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