Research On The Stability Of Fuzzy Systems

The stability analysis and design of fuzzy control systems have been the most important problems in fuzzy theory. The research of fuzzy control theory includes a series of main problems, such as the stability analysis, the system design approaches and the improvement of the system performance. It is difficult of the stability for fuzzy control because of nonlinearity of fuzzy systems. Up to now, there have existed a lot of measures to ensure the stability of fuzzy control systems. However the perfect theory system has not been formed. It is necessary to study the theoretical problems more deeply.This paper aims at the thorough research on the stability of fuzzy systems, and some innovations in the theory are obtained, which is of benefit to providing new thoughts and new methods for the investigation into fuzzy systems.First, this paper summarizes the development of fuzzy control systems, fuzzy large-scale systems and linear matrix inequality, and induces the correlative achievements of fuzzy control. It also sums up the theory's thoughtway and influence.Second, the method of the stability analysis of T-S fuzzy control systems is expatiated in this paper. The stability conditions of T-S fuzzy control systems of open-loop for continuous system and discrete system are given on the basis of Lyapunov theories. Then the stability conditions for closed-loop systems are proved.Third, the stability for diagonally dominant fuzzy dynamical system is discussed. The concept of generalized diagonally dominant fuzzy dynamical system is given, on the base of diagonally dominant fuzzy dynamical system. The sufficient conditions for the stability of this generalized diagonally dominant fuzzy dynamical system are proposed. Then the stability of fuzzy large-scale system is analysed, based on the idea of decomposition, reduce dimension of large-scale system, and the stability conditions are obtained.Finally, the quadratic stability problem of T-S fuzzy control systems is studied. Applying LMI technique in the linear matrix inequalities composed by the coefficient matrices of the subsystems, the interactions among the fuzzy subsystems were...