An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay.

*(English)*Zbl 1285.93054Summary: This paper is concerned with the stability of uncertain T-S fuzzy systems with interval time-varying delay. By uniformly dividing the delay interval into multiple segments and constructing an appropriate augmented Lyapunov-Krasovskii functional, some less conservative stability criteria are obtained, which include some existing results as special cases. Since a tighter bounding inequality is employed to deal with time-varying delay-dependent integral items, then some sources of computational complexity, such as the general convex combination and free weighting matrices are not necessary to be adopted in the derivation of our results. As a result, the developed criteria not only theoretically improve some existing results, but also have higher computational efficiency. Numerical examples are given to demonstrate the effectiveness of the proposed method.

##### MSC:

93C42 | Fuzzy control/observation systems |

93D30 | Lyapunov and storage functions |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |