This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.
Acknowledgements
The work described in this paper was partially supported the National Natural Science Foundation of China (Grant No. 60904004), the GRF: CityU 112809 of Hong Kong SAR Government, the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2009J020) and the grants from Chengdu Administration of Science and Technology (11DXYB212JH-027) and (11DXYB212JH-02).
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Yanbing Mao
Yanbing Mao received his BS degree from Liaocheng University, Shandong, China. He is currently pursuing an MS degree in University of Electronic Science and Technology of China, Chengdu, China. His research interests include fuzzy systems, switched systems and time-delay control systems. Hongbin Zhang
Hongbin Zhang received the BEng degree in Aerocraft Design from Northwestern Polytechnical University, Xi’an, China, in 1999, and the MEng and PhD degrees in Circuits and Systems from the University of Electronic Science and Technology of China, Chengdu, in 2002 and 2006, respectively. He has been with the School of Electrical Engineering, University of Electronic Science and Technology of China, since 2002, where he is currently a Professor. From August 2008 to August 2010, he has been serving as a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. His current research interests include fuzzy control, stochastic controland time-delay control systems.
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