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

Imen Iben Ammar, Hamdi Gassara, Ahmed El Hajjaji*, and Mohamed Chaabane
International Journal of Control, Automation, and Systems, vol. 20, no. 8, pp.2554-2568, 2022

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.

Keyword : Dynamic output-feedback controllers, line-integral polynomial fuzzy Lyapunov function, positive polynomial fuzzy model, Sum of Squares, uncertain interval systems.

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