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The analysis of asymptotic stability and stabilization of some classes of control systems with delay


A. A. Shestakov, О. N. Masina, О. V. Druzhinina

The work is devoted to research of asymptotic stability of controlled nonlinear systems, which are generalizations of Takagi-Sugeno systems on a case of delay. Global asymptotic stability of conditions of equilibrium states on the basis Lyapunov functions is studied. Stabilizing feedback is constructed. Takagi-Sugeno systems with delay are described by fuzzy rules of type IF…THEN and based on using of fuzzy controllers. Modification of system Takagi-Sugeno with delay on a case of matrixes with uncertainties is considered. Stability conditions of equilibrium states of the specified systems are obtained by the aid of Lyapunov-Krasovsky functionals. The obtained results can be used for working out approaches to designing and to improvement of technical control system.

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