Free-matrix-based integral inequality for stability analysis of uncertain T-S fuzzy systems with time-varying delay

This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with timevarying delay by delay-partitioning approach and Free-Matrix-based integral inequality. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then, on the basis of taking into account the independent upper bounds of the delay derivative in various delay intervals, some new results on tighter bounding inequalities, such as Peng-Park’s integral inequality and the Free-Matrix-based integral inequality are employed to effectively reduce the enlargement in bounding the derivative of LKF, therefore, less conservative results can be expected in terms of e s and LMIs. Finally, three numerical examples are included to show that the proposed method is less conservative than existing ones.