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Polynomial Dynamic Output-feedback Controllers for Positive Polynomial Fuzzy Systems with Time Delay

  • Control Theory and Applications
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International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper investigates the stability and stabilization problems of positive polynomial fuzzy uncertain interval models with time delay. Using the polynomial output feedback fuzzy control strategy, the design problem is firstly studied by considering the unmeasured states and measurable premise variables. Then, the control design problem is extended for both the unmeasurable states and unmeasurable premise variables. To study the considered analysis and design problems, a line-integral polynomial fuzzy Lyapunov function with polynomial terms depending of the estimated states is proposed. For each case, the proposed design conditions of the polynomial dynamic output feedback fuzzy controllers guarantying both the stability and the positivity of the resulting closed loop systems, are solved using the Sum of Squares (SOS) approach with tacking into account the positivity of the error signals. Finally, simulation examples are given to show the effectiveness of the proposed approaches.

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Authors and Affiliations

  1. National School of Engineers Sfax, Laboratory of Sciences and Techniques of Automatic Control & Computer Engineering, ENIS PB 1173, Sfax, 3038, Tunisia

    Imen Iben Ammar, Hamdi Gassara & Mohamed Chaabane

  2. Modeling, Information, and Systems (MIS) Laboratory, University of Picardie Jules Verne, 33 Rue St Leu, Amiens, 80000, France

    Ahmed El Hajjaji

Authors
  1. Imen Iben Ammar
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  2. Hamdi Gassara
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  3. Ahmed El Hajjaji
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  4. Mohamed Chaabane
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Correspondence to Ahmed El Hajjaji.

Additional information

Imen Iben Ammar received her engineering degree and Ph.D. degree in electrical engineering from the National School of Engineering of Sfax, University of Sfax, Tunisia, in 2015 and 2020, respectively. Her current research interests include analysis and control for polynomial fuzzy systems and positive polynomial fuzzy systems, observer based control for polynomial fuzzy systems, sum of squares approach, and delay systems.

Hamdi Gassara received his Ph.D. degree in automatic control from the University of Picardie Jules Vernes (UPJV), in 2011 and HDR degree from the University of Sfax, Tunisia, in 2019. Prior to his Ph.D., he received his Master’s 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 associate 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, and polynomial fuzzy model.

Ahmed El Hajjaji received his 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 Automatic control and Vehicle Research Group in MIS Lab (Modeling Information Systems Laboratory) with 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 350 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 received his Ph.D. degree in electrical engineering from the University of Nancy, Nancy, France, in 1991. He is currently a full 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 field 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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Ammar, I.I., Gassara, H., El Hajjaji, A. et al. Polynomial Dynamic Output-feedback Controllers for Positive Polynomial Fuzzy Systems with Time Delay. Int. J. Control Autom. Syst. 20, 2554–2568 (2022). https://doi.org/10.1007/s12555-020-0937-0

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