Abstract
In this paper, we consider the finite horizon $H_{2}/H_{\infty}$ control problem for linear stochastic differential equations (SDEs) with infinite Markovian jumps. A necessary and sufficient condition is proposed for the existence of the mixed $H_{2}/H_{\infty}$ control by means of the solvability of the coupled difference Riccati equations (CDREs). Moreover, the state feedback $H_{2}/H_{\infty}$ controller is constructed through the solution of CDREs.
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