Backward Stochastic H₂/H_∞ Control: Infinite Horizon Case

Abstract

The mixedH2/H∞control problem is studied for systems governed by infinite horizon backward stochastic differential equations (BSDEs) with exogenous disturbance signal. A necessary and sufficient condition for the existence of a unique solution to theH2/H∞control problem is derived. The equivalent feedback solution is also discussed. Contrary to deterministic or stochastic forward case, the feedback solution is no longer feedback of the current state; rather, it is feedback of the entire history of the state.

H2/H∞control for stochastic systems with delay

“…During the last decade, the problems of H 2 /H ∞ control for non-delay systems have been extensively investigated (see, for example, Zames (1981), Limbeer, Anderson, and Hendel (1984), Zhang, Zhang, and Chen (2006), Zhang (2014), and Wu and Zhang (2014)). Up * Email: sms_zhangqx@ujn.edu.cn to now, most of the results on H 2 /H ∞ control with delay are concentrated on deterministic systems; here, we list some representative works in this field as follows.…”