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Non-fragile robust stabilization and $H\infty$ control for uncertain stochastic nonlinear time-delay systems. (English) Zbl 1198.93189

Summary: This paper deals with the problem of non-fragile robust stabilization and $H\infty$ control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is 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 for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:
 93D15 Stabilization of systems by feedback 93B36 ${H}^{\infty }$-control 93E03 General theory of stochastic systems