Delay-range-dependent robust stabilisation and H_∞ control for nonlinear uncertain stochastic fuzzy systems with mode-dependent time delays and Markovian jump parameters

Abstract

This article focuses on the problems of robust stabilisation and H _∞ control for nonlinear uncertain stochastic systems with mode-dependent time delay and Markovian jump parameters represented by the Takagi–Sugeno (T-S) fuzzy model approach. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbances, Markovian jump parameters and unknown nonlinear disturbances. The purpose is to design a state feedback controller such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H _∞ performance level. Novel delay-range-dependent conditions in the form of linear matrix inequalities (LMIs) are derived for the solvability of robust stabilisation and H _∞ control problem. A desired fuzzy controller can be constructed by solving a set solutions of LMIs and can be easily calculated by Matlab LMI control toolbox. Finally, a numerical example is presented to illustrate the proposed method.

Keywords:

• robust H _∞ control
• stochastic fuzzy systems
• mode-dependent delays
• Markovian jump parameters
• linear matrix inequalities (LMIs)

Acknowledgements

The authors are very much thankful to all the referees for their valuable comments and suggestions for improving this article.