Robust Stochastic Stabilization and H ∞ Control for Neutral Stochastic Systems with Distributed Delays

Abstract

This paper considers the problem of robust stabilization and H ∞ control for a class of uncertain neutral stochastic systems, in which delay is distributed and the parametric uncertainties are norm-bounded. By designing a state feedback controller, we obtain a delay-dependent criterion such that the resulting closed-loop system is robustly stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions are presented based on the linear matrix inequality approach. Finally, numerical examples are used to illustrate the effectiveness and feasibility of the approaches proposed in this paper.

Delay-dependent robust H∞ control for uncertain stochastic systems with time-varying delays in state and control input

“…The stability analysis and controller design of stochastic systems has been an important topic of control theory, and a great number of results on these subjects have been reported in the literature. 14–24 For instance, by using Moon’s inequalities method, several sufficient conditions ensuring exponential stability in mean-square sense for stochastic time-delay systems were given in Chen et al 18 The problem of robust H ∞ control for uncertain stochastic systems with state delay was considered in Xu and Chen, 19 and a delay-independent H ∞ control scheme was proposed. In Chen et al, 21 Moon’s inequalities approach was applied to investigate the problem of delay-dependent robust stochastic stabilization and H ∞ control for stochastic systems with norm-bounded uncertainties and state delay.…”