Abstract 

This paper is concerned with stochastic H₂/H_∞ control problem for continuous-time stochastic differential systems with the diffusion coefficients depending explicitly on the state, control and disturbance as well as their expectations. A stochastic bounded real lemma of mean-field type is proved, which characterizes the equivalence between the H_∞ robust stability and the solvability of two coupled indefinite differential Riccati equations. This extremely critical result enables us to obtain sufficient and necessary conditions for the existence of H₂/H_∞ control for the underlying systems by virtue of the solvability of two sets of cross-coupled indefinite Riccati differential equations. Moreover, in the case that H₂/H_∞ control exists, the worst-case disturbance and the optimal control input admit a linear feedback forms of the state and its mathematical expectation, via the solutions to the two sets of coupled Riccati differential equations.