Abstract
For the stabilization problem of T-S fuzzy system, a new observer-based controller design approach is proposed when premise variables are not accessible. With a fuzzy observer, the estimated states error system is described as two parts: unknown premise variable caused terms and observer error terms. Consider the property that the norm of the unknown premise variable caused terms are under a Lipschitz condition constraint of observer error, an observer and controller errors augmented system is obtained. Then based on the Lyapunov function method, a series of linear matrix inequality conditions are proposed to asymptotically stabilize the system, the observer gain matrices are used to overcome the uncertainties caused by UPVs. Finally a simulation example is used to illustrate the effectiveness of the proposed method, comparisons with traditional method shows the conservatism reduction effects.
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Recommended by Associate Editor Huanqing Wang under the direction of Editor Euntai Kim. This work is supported in part by the National Natural Science Foundation of China (Grant No. 61803114, 61803127), the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province, China (Grant No. UNPYSCT-2017093), the Fundamental Research Funds for the Central Universities (Grant No. HEUCFJ180306).
Wen-Bo Xie received the B.E. and Ph. D. degrees from the Colloege of Automation, Harbin Engineering University, Harbin, China, in 2008 and 2013 respectively. He is currently a Lecturer with Harbin University of Science and Technology, Harbin, China. He was a Post-Doctoral Research Fellow with the University of Adelaide, Australia (2015-2016). He is currently with the College of Automation at Harbin University of Science and Technology, and a Post-Doctoral at Shang Hai University. His current research interests include T-S and polynomial fuzzy control systems.
He Li received the B.E.degree from the College of Automation, Qufu Normaly University, Rizhao, China, in 2016. He is currently pursuing the M.S.degree at Harbin University of Science and Technology, Harbin, China. His current research interests include T-S fuzzy control systems and multi-agent control.
Zhen-Hua Wang received his B.Sc. degree from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2008 and his M.Sc. and Ph.D. degrees from Harbin Institute of Technology, Harbin, China, in 2010 and 2014, respectively. From 2016 to 2017, he was a visiting scholar in the University of Adelaide, Adelaide, Australia. He is currently with the Department of Control Science and Engineering at Harbin Institute of Technology. His research interests include fault diagnosis and fault-tolerant control.
Jian Zhang received the B.E. and M.E. degrees from the College of Automation, Harbin Engineering University, Harbin, China in 2009 and 2012 respectively. She is working toward her Ph. D. degree in control science and engineering at the Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, China. Her research interests include diesel engine control, spacecraft formation coordinated control, finite-time control, and sliding mode control.
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Xie, WB., Li, H., Wang, ZH. et al. Observer-based Controller Design for A T-S Fuzzy System with Unknown Premise Variables. Int. J. Control Autom. Syst. 17, 907–915 (2019). https://doi.org/10.1007/s12555-018-0245-0
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DOI: https://doi.org/10.1007/s12555-018-0245-0