Harnessing membership function dynamics for output-feedback stabilization of T-S fuzzy systems

This paper presents a novel methodology for output-feedback stabilization of continuous-time Takagi–Sugeno (T-S) fuzzy systems, addressing local exponential stability and domain of attraction estimation. An augmented system integrates both the system and membership function dynamics. The membership function derivatives are modeled via a polytopic representation, capturing the local nature of the fuzzy system. A locally convergent iterative algorithm based on linear matrix inequalities is proposed to design a parallel distributed compensation controller that ensures a predefined decay rate and a domain of attraction estimate. A numerical example illustrates the advantages of the method over existing approaches, especially in the output-feedback case.