Enhanced relaxation-based local stabilization of T-S fuzzy systems: Achieving a simultaneous reduction in conservatism and complexity

This paper proposes an enhanced relaxation-based local stabilization framework for continuous-time T–S fuzzy systems that simultaneously reduces conservatism and computational complexity. In contrast to existing approaches, the proposed method eliminates the need for a priori assumptions or static transformations of the time derivatives of fuzzy basis functions, and enables a complete local stabilization procedure to be carried out entirely within the LMI framework. Moreover, by introducing a full row-rank canonical selection matrix, the number of slack variables is significantly reduced, thereby improving computational efficiency without sacrificing stability performance. Consequently, the resulting relaxation framework yields less conservative stabilization conditions and facilitates efficient controller synthesis for high-dimensional fuzzy systems. Finally, the effectiveness of the proposed method is demonstrated through two illustrative examples (i.e., cart-pendulum and mass–spring-damper examples), which show improved H∞ performance and substantial reductions in decision variables.