H ∞ control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

This paper is concerned with the H ∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input- and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities (HJIs), the exponential mean square H ∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly, by using fuzzy T-S model approach, the H ∞ controller can be designed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.