Stability of slowly varying Takagi-Sugeno fuzzy systems

Abstract

Presents a method for analyzing the stability of slowly varying Takagi-Sugeno fuzzy systems with linear submodels in the consequents of rules. This method can be used for both continuous-time and discrete-time systems and is based on transformation of the problem of stability of Takagi-Sugeno fuzzy systems to the problem of stability of polynomials with coefficients polynomically depending on weights of rules. It is supposed that the plant is described by the Takagi-Sugeno fuzzy system with linear state-space or input-output submodels in the consequents of rules and the controller by the Takagi-Sugeno fuzzy system with linear state feedback submodels or dynamic output feedback controllers in the consequents of rules. The problem of the stability analysis of such systems can be transformed to the problem of the stability analysis of polynomials with polynomic structure of its coefficients. This problem can be solved by the modified Jury (for discrete-time systems) or by the modified Routh or Hurwitz criterion (for continuous-time systems).