ABSTRACT
This chapter discusses the H∞ analysis problem for a general class of nonlinear stochastic systems with time-delays, which are described by general stochastic functional differential equations. It describes that the Razumikhin-type method is used to establish some certain conditions to achieve the H∞ performance. The Razumikhin-type method and Hamilton–Jacobi–Bellman(HJB) inequality theory are employed to obtain some easy-to-test criteria, which are used to determine whether the stochastic system under investigation is internally stochastic stable and whether a prescribed H∞ performance level is satisfied. The chapter explains the methodology to deal with the L2 gain problem for a special class of stochastic differential delay systems. General conditions are derived under which the L2 gain of the system is less than or equal to a given constant, and some easy-to-test criteria are subsequently given, which can be used to check the stability and determine the H∞ performance index of the system.
