Extended dissipative analysis for T–S fuzzy system with sampled-data input and actuator fault

Abstract

This paper is concerned with reliable robust sampled-data control for T–S fuzzy system with time-varying delay. By adjusting the free weight matrix in the concept of extended dissipative, $H_{\mathrm{\infty }}$, $L_2-L_{\mathrm{\infty }}$, passive and $(Q,S,R)$-dissipative performance are solved in a unified framework. A novel mode-dependent Lyapunov–Krasovskii functional (LKF) is constructed, which fully utilises the characteristics of the real sampling period. Based on Lyapunov stability theory, Newton–Leibniz condition and new integral inequality techniques, some less conservative sufficient conditions are obtained to guarantee the close-loop system is asymptotically stable and extended dissipative. Based on sampled-data approach, a robust reliable controller can be developed by solving the linear matrix inequalities (LMIs). The advantage and effectiveness of the proposed design method can be illustrated by several numerical examples.

Keywords:

• T–S fuzzy system
• sampled-data control
• extended dissipative
• actuator fault
• linear matrix inequalities (LMIs)

Acknowledgements

This work is partially supported by the National Natural Science Foundation of China No. 61273004, and the Natural Science Foundation of Hebei Province No. F2018203099.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China No. 61273004, and the Natural Science Foundation of Hebei Province No. F2018203099.

Notes on contributors

Huan Yu

Huan Yu (1994–), Tianjin, China, postgraduate, mainly engaged in fuzzy control research.

Yuechao Ma

Yuechao Ma (1963–), Liaoning Province, China, doctor, professor, mainly engaged in fuzzy nonlinear system control research.

Junwei Liu

Junwei Liu (1984–), Shandong Province, China, doctor, privatdozent, mainly engaged in functional analysis.