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Stability analysis based on Lyapunov functions and LMI conditions for discrete control systems with fuzzy controllers


О. N. Masina, О. V. Druzhinina, V. I. Afanasyeva

This paper examines some modification discrete control systems with fuzzy controllers described by fuzzy Takagi-Sugeno model. If rules consist of fuzzy propositions IF…THEN form where consequent part THAN is singleton (i.e. one-element set) then such control system belongs to singleton type. Equilibrium stability conditions are derived for the singleton type control systems. Lyapunov functions approach is used to the stability analysis. Based on Lyapunov functions method and a linear matrix inequality (LMI) approach, equilibrium stability conditions for open-loop and closed-loop Takagi-Sugeno fuzzy discrete systems are presented. Fuzzy controller design procedure to stabilize discrete system is proposed. Intellect control systems classification is presented and it is shown a location of fuzzy control among intellect systems. The stability conditions which were derived in this paper may be utilized to fuzzy controllers design, stability and stabilization problems, and technical control systems design based on fuzzy rules.

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