Stabilization of Discrete-Time T–S Fuzzy Positive Systems with Multiple Delays

  • Abdellah BenzaouiaEmail author
  • Ahmed El Hajjaji
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 8)


This chapter deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The results are presented under the linear Programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of LP for unbounded control case. The obtained result is then extended to the stabilization problem by nonnegative control and stabilization by bounded control. The stabilization conditions are derived using the single Lyapunov–Krasovskii Functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. To show the merit of the proposed method, a comparison between LP and LMI approaches is presented upon a second example.


Discrete-time Fuzzy Systems Lyapunov-Krasovskii Functional (LKF) Output Feedback Control Nonnegative Control Real Plant Model 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of Cadi AyyadMarrakechMorocco
  2. 2.Laboratoire de Modélisation, Information et SystèmesUniversité de Picardie Jules VerneAmiensFrance

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