Nonlinear Stochastic H 2 /H ∞ Control with (x, u, v) -Dependent Noise: Infinite Horizon Case.

For general nonlinear stochastic Ito systems with state, control and external disturbance-dependent noise, the infinite horizon mixed H 2 / H ∞ control is studied. It turns out that in order to solve the H 2 /H ∞ control, one only needs to solve four cross-coupled Hamilton-Jacobi equations. A necessary condition and a sufficient condition for the existence of the solution of H 2 /H ∞ control is respectively presented, which extends the previous results to more general models.