In this paper, we study the stability of fuzzy control systems of Takagi–Sugeno-(T–S) type
based on the classical theory of Lie algebras. T–S fuzzy systems are used to model
nonlinear systems as a set of rules with consequents of the type x˙(t)= Alx (t)+ Blu (t). We
conduct the stability analysis of such T–S fuzzy models using the Lie algebra LA generated
by the Al matrices of these subsystems for each rule in the rule base. We first develop our
approach of stability analysis for a commuting algebra LA, where all the consequent state …