Some remarks on stochastic H∞ control of linear and nonlinear Itô-type differential systems

This paper studies linear and nonlinear stochastic H_∞ control of Itô-type stochastic differential systems with all the state, control input and external disturbance-dependent noise. For general linear stochastic systems with random coefficients, it is shown that the mixed H₂/H_∞ design as well as the sole H_∞ design is associated with the solvability of some coupled backward stochastic differential equations (BSDEs). By means of Hamilton-Jacobi inequalities, the nonlinear stochastic H_∞ control with deterministic coefficients and (x, u, v)-dependent noise is extensively investigated.