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Optimal guaranteed cost control for an uncertain discrete T-S fuzzy system with time-delay

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Abstract

This paper considers the guaranteed cost control problem for a class of uncertain discrete T-S fuzzy systems with time delay and a given quadratic cost function. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequalities (LMI) approach by constructing a specific nonquadratic Lyapunov-Krasovskii functional and a nonlinear PDC-like control law. A convex optimization problem is also formulated to select the optimal guaranteed cost controller that minimizes the upper bound of the closed-loop cost function. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approaches.

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Authors and Affiliations

  1. College of Electrical Engineering and Information Technology, Three Gorges University, Yichang, Hubei, 443002, China

    Renming Wang

  2. LAMIH, UMR CNRS, Université de Valenciennes et du Hainaut-Canbrésis, Le Mont Houy, Valenciennes Cedex, France

    Thierry Marie Guerra

  3. Key Laboratory of Measurement and Control of CSE of Ministry of Education, Southeast University, Nanjing, Jiangsu, 210096, China

    Juntao Pan

Authors
  1. Renming Wang
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  2. Thierry Marie Guerra
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  3. Juntao Pan
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Corresponding author

Correspondence to Renming Wang.

Additional information

This work was supported by the Natural Science Foundation of Hubei Province (No.2007ABA361).

Renming WANG was born in Xiantao, Hubei Province in 1964. He received his B.S. degree in Applied Mathematics, and both his M.S. and Ph.D. degrees in Control Theory and Control Engineering. He is currently a professor of Control Theory at Three Gorges University (CTGU). He visited the University of Valenciennes, France from March 2005 to September 2005. He is a member of the IFAC Technical Committee 3.2 “Cognition and Control”. His major research interests include switched system, fuzzy control, optimal control, impulsive control.

Thierry Marie GUERRA was born in Mulhouse, France in 1963. He is currently a professor at the University of Valenciennes et du Hainaut-Cambrésis (UVHC), France. He received his Ph.D. degree in Automatic Control from the UVHC in 1991 and the HDR in 1999. He is a deputy manager of the Laboratoire d’Automatique, de Mécanique et d’Informatique Industrielles et Humaines (LAMIH UMR CNRS 8530, more than 200 researchers and Ph.D. students) and also heading the System Modeling and Control Research Group. He is also a deputy manager of the GRAISyHM (Research group in Integrated Automation and Man-Machine systems, 220 researchers from 10 labs of Region Nord Pas de Calais, France). He is a member of IEEE Vehicle Power and Propulsion Committee, vice-chair of the IFAC Technical Committee 3.2 “Cognition and Control” and member of the IFAC TC 7.1 “Automotive Control”. His major research fields and topics of interest are, nonlinear control, fuzzy control, optimal control, and their applications to power train systems.

Juntao PAN was born in 1983. He now is a Ph.D. candidate in the Research Institute of Automation at Southeast University, Nanjing. His current research interests include multiple models switching control and fuzzy control.

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Wang, R., Guerra, T.M. & Pan, J. Optimal guaranteed cost control for an uncertain discrete T-S fuzzy system with time-delay. J. Control Theory Appl. 7, 144–150 (2009). https://doi.org/10.1007/s11768-009-7280-6

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  • DOI: https://doi.org/10.1007/s11768-009-7280-6

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