In this note, we consider the finite horizon mixed H 2 / H ∞ control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. Firstly, we derive a stochastic bounded real lemma (SBRL), which is used to establish a necessary and sufficient condition for the existence of the mixed H 2 / H ∞ control via the solvability of four coupled difference matrix-valued recursions (CDMRs). Moreover, a state feedback H 2 / H ∞ controller is designed by means of the solutions of CDMRs.
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Hou et al. (2010) studied this question.
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