Guaranteed Cost Control of Impulsive Nonlinear Stochastic Systems With Mixed Time Delays

Abstract

This article mainly addresses the guaranteed cost control (GCC) problem for a class of impulsive nonlinear stochastic systems with mixed time delays, where both distributed time delay as well as discrete time delay are considered. Utilizing the Hamilton–Jacobi inequalities technique, Lyapunov–Krasovskii functional (LKF) and stochastic control theory, a new delay‐dependent sufficient condition is acquired to ensure the asymptotic stability in probability (ASP) of the closed‐loop system (CLS). Moreover, the guaranteed cost controller is designed and the upper bound of cost function is given. At the same time, three corollaries are presented for the special circumstance without impulse, distributed time delays or time‐varying time delay, respectively. Finally, the feasibility of the theoretical results is verified by an example.