О.V. Druzhinina, O.N. Masina

The article is devoted to analysis of stability of systems with fuzzy controllers. For indicated systems conclusions are carried out by calculation of characteristic values of output linguistic variable through characteristic values of input linguistic variables under the logic formulas using logic operations AND and OR. Transfer from linguistic variables is made through corresponding characteristic functions - functions of membership. Development of algorithm of fuzzy control contains the following procedures: fuzzification; designing of fuzzy rules of type IF - THEN; obtaining of fuzzy value of output variable in the form of degrees of membership of its terms; defuzzification. For research of stability of technical systems with fuzzy controllers the geometrical method based on studying of vector fields of object of control is used in the paper. One-dimensional, two-dimensional and n-dimensional (n  3) cases are considered. Stability conditions of an equilibrium state of one-dimensional fuzzy system are received. The notion «stability stock» for studied systems with fuzzy controllers is introduced and studied. The algorithm of a finding of stability stock of n-dimensional (n  3) fuzzy systems of control is developed. The obtained results can be used at designing of controlled technical systems on the basis of fuzzy rules and expert estimations.