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Local stabilization of Polynomial Fuzzy Model with time delay: SOS approach

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Abstract

In this paper, a design method of control for Polynomial Fuzzy Models (PFM) with time delay is developed. By using a Polynomial Lyapunov Krasovskii Functional (PLKF) with double integral and by imposing bounds on the derivatives of each state, less conservative sufficient conditions are established to ensure the local stability of the closed loop system. Furthermore, a Domain Of Attraction (DOA) in which the initial states are ensured to converge asymptotically to the origin is estimated. The resulting conditions are formulated in terms of Sum-Of- Squares (SOS) which can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. Some examples are provided to show the effectiveness and the merit of the design procedure.

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Authors and Affiliations

  1. University of Picardie Jules Verne, MIS Lab, F80000, Amiens, France

    Hamdi Gassara & Ahmed El Hajjaji

  2. National School of Engineers Sfax, STA Lab, Sfax, Tunisia

    Hamdi Gassara, Fatma Siala & Mohamed Chaabane

Authors
  1. Hamdi Gassara
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  2. Fatma Siala
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  3. Ahmed El Hajjaji
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  4. Mohamed Chaabane
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Corresponding author

Correspondence to Ahmed El Hajjaji.

Additional information

Recommended by Associate Editor Ho Jae Lee under the direction of Editor Euntai Kim. This journal was supported by the Korean Federation of Science and Technology Societies Grant.

Hamdi Gassara received the Ph.D degree in automatic control from the University of Picardie Jules Vernes (UPJV), in 2011. Prior to his Ph.D., he received his Master degree from UPJV in 2008. His teaching experience started when he was a Ph.D. student in UPJV France from 2008 to 2011. He is currently an assistant professor in Electrical department at National School of Engineering of Sfax, Tunisia. His research focuses on analysis and control for fuzzy model with time delay, fault tolerant control, diagnostics, saturations, polynomial fuzzy model.

Fatma Siala received her Master degree in 2011 from the National School of Engineering of Sfax, Tunisia, where she is currently working toward a Ph.D. degree. Her current research interests include polynomial fuzzy systems, sum of squares approach and delay systems.

Ahmed El Hajjaji received the Ph.D. degree in automatic control and HDR degree from the University of Picardie Jules Verne (UPJV), France in 1993 and 2000, respectively. He is currently a full professor and head of the research team of control in MIS Lab (Modeling Information Systems Laboratory) of UPJV. He has been the director of the Professional Institute of Electrical Engineering and Industrial Computing from 2006 to 2012. Since 1994, he has published more than 259 Journal and conference papers in the areas of advanced fuzzy control, fault detection and diagnosis and fault tolerant control and their applications to vehicle dynamics, engine control, power systems, renewable energy conversion systems and to industrial processes. His research interests include fuzzy control, vehicle dynamics, fault-tolerant control, neural networks, maglev systems, and renewable energy conversion systems.

Mohamed Chaabane was born in Sfax, Tunisia, on August 26, 1961. He received the Ph.D. degree in electrical engineering from the University of Nancy, Nancy, France, in 1991. He is currently a Professor with the National School of Engineering, University of Sfax, where he has been a Researcher with the Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA) since 1997. The main research interests are in the filed of robust and optimal control, fault tolerant control, delay systems, descriptor systems, fuzzy logic systems and applications of these techniques to fed-batch processes, asynchronous machines, agriculture systems and renewable energy. Currently, he is an associate editor of the International Journal on Sciences and Techniques of Automatic Control and Computer Engineering (www.sta-tn.com).

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Gassara, H., Siala, F., El Hajjaji, A. et al. Local stabilization of Polynomial Fuzzy Model with time delay: SOS approach. Int. J. Control Autom. Syst. 15, 385–393 (2017). https://doi.org/10.1007/s12555-014-0575-5

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  • DOI: https://doi.org/10.1007/s12555-014-0575-5

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