Regular Papers

International Journal of Control, Automation and Systems 2017; 15(1): 385-393

Published online December 23, 2016

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

© The International Journal of Control, Automation, and Systems

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

Hamdi Gassara, Fatma Siala, Ahmed El Hajjaji*, and Mohamed Chaabane

University of Picardie Jules Verne

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.

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

Article

Regular Papers

International Journal of Control, Automation and Systems 2017; 15(1): 385-393

Published online February 1, 2017 https://doi.org/10.1007/s12555-014-0575-5

Copyright © The International Journal of Control, Automation, and Systems.

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

Hamdi Gassara, Fatma Siala, Ahmed El Hajjaji*, and Mohamed Chaabane

University of Picardie Jules Verne

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.

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

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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