ABSTRACT
This chapter presents some research topics on stochastic H 2/H∞control. Stochastic Itô systems with random coefficients have important applications especially in mathematical finance, and the corresponding stochastic LQ control can be found. It seems that the reference first started to consider the H∞ control of Itô-type differential equations with random coefficients. The chapter explores the H2/H∞ control of, where the external disturbance is considered in mathematical modeling, which is very realistic in comparison with the sole LQ control. Although the nonlinear continuous-time stochastic H8 control, mixed H2/H∞ control and filtering have been basically solved, there is an essential difficulty in the study of the H2/H∞ control and filtering of nonlinear discrete time stochastic systems with multiplicative noise. The classical LaSalle theorem describes the limit behavior of dynamic systems, which is a seminal work in stability theory.
