Nonlinear Stochastic H₂/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 H2/Hinfincontrol is studied. It turns out that in order to solve the H2/Hinfincontrol, 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 H2/Hinfincontrolis respectively presented, which extends the previous results to more general models.