Abstract
This paper addresses the robust H∞ static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainH∞ performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 61522306). The authors are grateful to the Editor-in-Chief, the Associate Editor, and anonymous reviewers for their constructive comments based on which the presentation of this paper has been greatly improved.
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Shasha Fu received the BE degree in automation from Northeast Forestry University, China in 2012 and the ME degree in control science and engineering from Harbin Institute of Technology (HIT), China in 2014. She is currently pursuing the PhD degree in the Research Institute of Intelligent Control and Systems, HIT. Her research interests include fuzzy control, robust filtering and control, nonlinear systems, fault-tolerant control, and their engineering applications.
Jianbin Qiu received the BE and PhD degrees in mechanical and electrical engineering from the University of Science and Technology of China (USTC), China in 2004 and 2009, respectively. He also received the PhD degree in mechatronics engineering from the City University of Hong Kong, China in 2009. He has been with the School of Astronautics, Harbin Institute of Technology since 2009, where he is currently a full professor. Prof. Qiu is a senior member of IEEE and serves as the chairman of the IEEE Industrial Electronics Society Harbin Chapter, China. He is an associate editor of IEEE Transactions on Cybernetics. His current research interests include intelligent and hybrid control systems, signal processing, and robotics. He is the awardee of the NSFC Excellent Young Scholars Program in 2015.
Wenqiang JI received the Bachelor’s degree in automation from the Harbin Engineering University, China in 2012. He is currently pursuing his PhD in control science and engineering at School of Astronautics, Harbin Institute of Technology, China. His main research fields include fuzzy systems and control, robust control, and sliding-mode control.
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Fu, S., Qiu, J. & Ji, W. Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions. Front. Comput. Sci. 11, 937–947 (2017). https://doi.org/10.1007/s11704-016-6138-6
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DOI: https://doi.org/10.1007/s11704-016-6138-6