一类具有两个加性时变时滞系统的稳定性分析

Stability analysis on a class of systems with two additive time-varying delays

为了研究具有两个加性时变时滞系统的稳定性问题,采用动态时滞分解法将每个时滞的变化区间划分为两个不等的子区间。在每个子区间上构造合适的Lyapunov-Krasovskii(L-K)泛函,利用积分不等式和倒数凸方法处理L-K泛函的导数,得到基于线性矩阵不等式的稳定性判据。与已有判据相比,所提出的判据具有较小的保守性和较低的复杂度。数值算例验证了本文结果的优越性。

The stability of the systems with two additive time-varying delays is studied,the dynamic time-delay decomposition method is used to divide each delay variation interval into two unequal subintervals,and suitable Lyapunov-Krasovskii(L-K)functionals are constructed on each subinterval.The stability criteria based on linear matrix inequality are obtained by using integral inequality and reciprocal convex method to deal with the derivatives of the L-K functionals.Compared with the existing criteria,the proposed criteria are less conservative with lower numerical complexity.A numerical example is given to verify the superiority of the proposed results.