Nonlinear Stochastic $H_2/H_\infty$ Control with $(x,u,v)$

For general nonlinear stochastic Ito systems with state, control and external disturbance-dependent noise, the infinite horizon mixed H₂/H_infin control is studied. It turns out that in order to solve the H₂/H_infin 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 H₂/H_infin controlis respectively presented, which extends the previous results to more general models.