Backward stochastic H 2 / H ∞ control: Infinite horizon case

Abstract

The mixed H 2 / 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 the H 2 / 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. © 2014 Zhen Wu and Qixia Zhang.