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Stability Analysis and Memory Control Design of Polynomial Fuzzy Systems with Time Delay via Polynomial Lyapunov-Krasovskii Functional

Hamdi Gassara, Ahmed El Hajjaji*, Mohamed Krid, and Mohamed Chaabane
International Journal of Control, Automation, and Systems, vol. 16, no. 4, pp.2011-2020, 2018

Abstract : "This paper investigates the problems of delay-dependent stability analysis and memory control design of polynomial fuzzy systems with time delay. Using polynomial Lyapunov-Krasovskii functional and slack polynomial matrix variables, delay dependent sufficient stability and stabilizability conditions are derived in terms of sum of squares (SOS) which can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. The main advantage of the proposed design is the reduction of conservatism for three great reasons. The first one is that polynomial matrices are not only dependent on the system state vector but also on the state vector with time delay. The second one is that the design conditions are formulated in delay dependent SOS. It is well known that the delay-dependent conditions are less conservative than those independent of time delay. The third one is that only correlated terms are used in the design of SOS. The simulation and comparison are given to illustrate the lesser conservativeness of the proposed result."

Keyword : "Polynomial Lyapunov Krasovskii functionnal, polynomial fuzzy systems, sum of squares (SOS), time delay."

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