Backward Stochastic H 2 /H ∞ Control with Random Jumps

This paper is concerned with H 2 / H ∞ control of a new class of stochastic systems. The most distinguishing feature, compared with the existing literature, is that the systems are described by backward stochastic differential equations ( BSDEs ) with B rownian motion and random jumps. It is shown that the backward stochastic H 2 / H ∞ control under consideration is associated with theL 2 -gain of the corresponding uncontrolled backward stochastic perturbed system. A necessary and sufficient condition for the existence of a unique solution to the control problem under consideration is derived. The resulting solution is characterized by the solution of an uncontrolled forward backward stochastic differential equation ( FBSDE ) with B rownian motion and random jumps. When the coefficients are all deterministic, the equivalent linear feedback solution involves a pair of Riccati‐type equations and an uncontrolled BSDE . In addition an uncontrolled forward stochastic differential equation ( SDE ) is given.