Nonlinear Stochastic $H_2/H_\infty$ 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
_infin
control is studied. It turns out that in order to solve the H
₂
/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 H
₂
/H
_infin
controlis respectively presented, which extends the previous results to more general models.