A nonmonotonically decreasing relaxation approach of Lyapunov functions to guaranteed cost control for discrete fuzzy systems

This study presents a nonmonotonically decreasing relaxation approach of Lyapunov functions to guaranteed cost control for discrete Takagi–Sugeno (T–S) fuzzy systems. First, the authors summarise the previous results on a relaxation of nonmonotonically decreasing of Lyapunov functions, and newly derive one lemma based on the previous results. Based on the newly derived lemma, they propose guaranteed cost control design for discrete T–S fuzzy systems. The design conditions can be represented in terms of linear matrix inequalities and provide more relaxed results than the existing approach. A design example is included to demonstrate the relaxation effectiveness of the proposed approach in guaranteed cost control.