Fuzzy Logic Control System Stability Analysis Based on Lyapunov’s Direct Method


  • Radu-Emil Precup "Politehnica" University of Timi¸soara Department of Automation and Applied Informatics
  • Marius-Lucian Tomescu "Aurel Vlaicu" University of Arad Computer Science Faculty Complex Universitar M, Str. Elena Dragoi 2, RO-310330 Arad, Romania
  • Ștefan Preitl "Politehnica" University of Timi¸soara Department of Automation and Applied Informatics Bd. V. Parvan 2, RO-300223 Timi¸soara, Romania


fuzzy logic controller, LaSalle’s invariance principle, Lyapunov function candidate


A stability analysis method for nonlinear processes controlled by Takagi- Sugeno (T-S) fuzzy logic controllers (FLCs) is proposed. The stability analysis of these fuzzy logic control systems is done in terms of Lyapunov’s direct method. The stability theorem presented here ensures sufficient conditions for the stability of the fuzzy logic control systems. The theorem enables the formulation of a new stability analysis algorithm that offers sufficient stability conditions for nonlinear processes controlled by a class of T-S FLCs. In addition, the paper includes an illustrative example that describes one application of this algorithm in the design of a stable fuzzy logic control system.


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