Stability analysis of type-2 fuzzy logic controllers

Abstract

The application of the direct Lyapunov method to the stability analysis of systems controlled by type-2 fuzzy logic controllers (FLC) is presented. The method is an extension of a method proposed for type-1 fuzzy systems. It is usually applied to systems described by state equations and controlled by fuzzy controllers using state variables as inputs but has been extended to controllers that have the error and the integral of error of the controlled variable as inputs. The proposed method allows to modify the controller rule base so that the controlled system is stable in the operating range defined by the manipulative variable constraints. The method is applied to the stability analysis of a bioreactor and of a CSTR controlled by type-2 FLCs.