State and output feedback’s finite-time guaranteed cost [formula omitted] control for uncertain nonlinear stochastic systems with time-varying delays

Abstract

The problems of guaranteed cost control and H∞ control are studied in this paper for nonlinear uncertain Itô’s stochastic systems with time-varying delays in finite-time. It is assumed that the nonlinear function in the systems satisfies the quasi-one-sided Lipschitz nonlinear constraint condition, which is weaker and less conservative than the one-sided Lipschitz condition. Some novel sufficient conditions for the existence of guaranteed cost control strategies are derived by using the Gronwall’s inequality, Dynkin’s formula, and Lyapunov–Krasovskii functional. The state and output feedback’s controllers based on event-triggered control guarantee that the closed-loop system is finite-time stochastically bounded and the given quadratic cost function has an upper bound. Finally, the effectiveness of the suggested method is illustrated by numerical simulation.