Finite horizon H2/H∞ control for SDEs with infinite Markovian jumps

This paper concerns the finite horizon H-2/H-infinity control for a broad class of linear It (o) over cap 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 H-2/H-infinity control. Moreover, an iterative algorithm is given to solve GDREs. (C) 2019 Elsevier Ltd. All rights reserved.