Robust Control for Stochastic Nonlinear Delay Systems with Jumps

Abstract

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 HamiltonJacobi 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.