一类时变时滞系统改进的稳定性准则

Improved Stability Criterion for a Class of Time-varying Delayed Systems

研究一类时变时滞系统稳定性准则的改进问题。首先,基于李雅普诺夫稳定性理论,充分利用时滞信息,通过引入增广矩阵和改进的三重积分项来构造Lyapunov-Krasovskii(L-K)泛函;其次,应用Wirtinger积分不等式结合凸组合不等式来处理L-K泛函求导过程中产生的积分项,以线性矩阵不等式的形式得到了一个保守性较小和运算效率较高的稳定性准则;最后,通过一个通用的数例验证所得准则的有效性。

This paper investigates the stability criterion for a class of time-varying delay systems.Firstly,based on Lyapunov stability theory and the delay information,the Lyapunov-Krasovskii(L-K)functional is constructed by introducing an augmented matrix and triple integral.Secondly,the integral terms from the derivation of Lyapunov-Krasovskii functional are dealt with by Wirtinger integral inequality and convex combination inequality.Finally,stability criterion for time-varying delay systems with less conservatism and high computational efficiency are obtained in the form of LMIs.The effectiveness of the proposed method is verified by a well-known numerical example in prevailing literature.