Stochastic H2/H∞ control with state-dependent noise

For a system governed by Itô-type nonlinear stochastic differential equation with state-dependent noise, the H2/H∞ control problem is considered, which combines the H2 optimization with the robust H∞ performance. A cross-coupled Hamilton-Jacobi equations associated with the nonlinear stochastic H2/H∞ control are obtained, based on which, sufficient conditions for designing the finite and infinite horizon nonlinear stochastic H2/H∞ controllers are derived. Some results on linear stochastic H2/H∞ control can be viewed as corollaries of this paper.