Delay-dependent robust ℋ_∞ control for uncertain stochastic time-delay system

Abstract

This article deals with the problem of robust stabilisation and ℋ_∞ control for a class of uncertain stochastic time-delay system. The parametric uncertainties are real time-varying and norm bounded. The aim is to design a memoryless state-feedback control law such that the closed-loop system are 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 for the existence of such control law are presented based on the linear matrix inequalities approach. Numerical examples are given to illustrate the effectiveness of the developed techniques.

Keywords:

• stochastic system
• time-delay
• ℋ_∞ control
• linear matrix inequalities (LMIs)
• norm-bounded uncertainties

Acknowledgements

The authors would like to thank the reviewers for their very helpful comments and suggestions, which have improved the presentation of the article. The work of Yuanqing Xia was supported by the National Natural Science Foundation of China under Grant 60504020 and Excellent young scholars Research Fund of Beijing Institute of Technology 2006y0103, respectively.