Robust Control for Stochastic Nonlinear Delay Systems with Jumps

The problem of infinite horizon H∞ control for general delayed nonlinear stochastic Markov jump systems with the infinite jumping parameters is considered in this paper, in which the noise is dependent on the state, control, and external disturbance. The coupled Hamilton–Jacobi inequalities (HJIs)-based sufficient condition is given to ensure the existence of the H∞ controller. As a corollary, infinite horizon H∞ controllers are designed for nonlinear stochastic time-delay systems without jumps by solving a series of coupled HJIs. Besides, the effectiveness of the proposed method is verified by a numerical example.