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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
  • Mohamed Chaabane
Regular Papers Intelligent Control and Applications
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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.

Keywords

Polynomial Lyapunov Krasovskii functionnal polynomial fuzzy systems sum of squares (SOS) time delay 

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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Hamdi Gassara
    • 1
  • Ahmed El Hajjaji
    • 2
  • Mohamed Krid
    • 3
    • 4
  • Mohamed Chaabane
    • 1
  1. 1.National School of Engineers SfaxSTA LabSfaxTunisia
  2. 2.University of Picardie Jules Verne, MIS LabAmiensFrance
  3. 3.Industrial Engineering Department, College of EngineeringKing Saud UniversityRiyadhSaudi Arabia
  4. 4.Raytheon Chair for Systems Engineering (RCSE Chair), Advanced Manufacturing InstituteKing Saud UniversityRiyadhSaudi Arabia

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