O.N. Masina

The article is devoted to development of methods of designing of the controllers which are carrying out process of development of controlling influences on the basis of knowledge of fuzzy judgements of type IF - THEN. The first step of designing of controllers is construction of base of the rules which are association of fuzzy rules of type IF - THEN. The second step is transfer of current values of input variables of fuzzy controller in linguistic degree of membership. This step is called as procedure of fuzzification. A following step of designing of the controllers is development of the solution in the form of fuzzy set in the form of resultant membership function. Definition for resultant membership of a output linguistic variable - controlling influence on object of control - is called as procedure defuzzification in which result the fuzzy conclusion will be transformed to crisp number. Feature of research of stability of fuzzy controllers consists that the controller possesses property at which division of phase space (space of state) into areas (cells) for which parameters of a controller and its structure are depending on area is possible. The majority of stability controllers suppose quadratic Lyapunov's function. However when the number of subsystems increases, important there is a volume of calculations, and existence or a finding of comprehensible function of Lyapunov isn't guaranteed, though the controller and is actually stability. To overcome the specified lack, for research of stability of fuzzy controllers in article are used piecewise quadratic Lyapunov's functions. The obtained results can be used for improvement of technological processes and technical systems of fuzzy control.

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