Abstract
This paper concerns the finite horizon H2∕H∞ control for a broad class of linear Itô stochastic differential equations (SDEs) with infinite Markovian jumps and (x,u,v)-dependent noise. We derive stochastic bounded real lemma (SBRL) and linear quadratic (LQ) optimal control result for the considered system at first. Further, a necessary and sufficient condition, which is represented by the solution of a countably infinite set of coupled generalized difference Riccati equations (GDREs), is proposed for the existence of the mixed H2∕H∞ control. Moreover, an iterative algorithm is given to solve GDREs.
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