Stochastic H2/H∞ Control with Random Coefficients

This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefcients,which is actually a control combining the H2 optimization with the H∞robust performance as the name of H2/H∞ reveals.Based on the classical theory of linear-quadratic(LQ,for short)optimal control,the sufcient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation(BSRE,for short)associated with H∞ robustness are derived.Then the sufcient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Riccati equations.