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Local Stabilization of Polynomial Fuzzy Model with Time Delay: SOS Approach

Hamdi Gassara, Fatma Siala, Ahmed El Hajjaji*, and Mohamed Chaabane
International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp.385-393, 2017

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."

Keyword : "Domain Of Attraction (DOA), local stability, polynomial fuzzy systems, polynomial Lyapunov Krasovskii functional, sum of squares (SOS), time delay."

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