Research ArticleFurther improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by delay-partitioning approach

- By combining delay-partitioning approach with the Free-Matrix-Based integral inequality, this paper mainly focuses on further improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay.
- A modified complete delay-partitioning augmented LKF is established by partitioning the delay in all integral terms.
- The time-varying delay τ(t)-dependent and [Xij]m×m-dependent sub-LKFs are also introduced to the augmented LKF.
- By means of employing some new results on tighter bounding inequalities such as Peng-Park׳s integral inequality and Free-Matrix-Based integral inequality, less conservative results can be achieved in terms of es and LMIs.

This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by a delay-partitioning approach. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then some tighter bounding inequalities, i.e., Peng-Park׳s integral inequality (reciprocally convex approach) and the Free-Matrix-Based integral inequality (which yields less conservative stability criteria than the use of Wirtinger-based inequality does) are introduced to reduce the enlargement in bounding the derivative of LKF as much as possible, therefore, less conservative results can be expected in terms of es and LMIs. Finally, a numerical example is included to show that the proposed methods are less conservative than existing ones.