基于Wirtinger的区间时滞系统的稳定性分析

Stability Analysis for Systems with Interval Time-Varying Delay Based on Wirtinger-Based Integral Inequality

为了解决区间时变时滞系统的稳定性问题,本研究通过使用合适的L-K泛函,推导方式上采用Wirtinger积分不等式和改进的Jensen型不等式相结合的方法,得到了基于线性矩阵不等式LMI的区间时变时滞系统稳定性的新判据,并使用Matlab求解,同时给出数值例子进行验证。验证结果表明,当d=0.3和d未知时,本文结果与文献[11]和[15]相比具有更小的保守性;当d=0.1时,与文献[14]相比保守性较大,但当时滞导数d=0.3,d=0.5,d=0.8时,与文献[14]相比,本文方法能获得更好的时滞上界。说明本文结果在时滞导数项比较大时与当前一些方法相比具有较好的优越性。

In order to solve the problem of the stability of time varying delay systems, this paper provides a combined method of Wirtinger-based integral inequality and improved Jensen type inequality, by using a suitable L-K Functional. A new criterion for stability of time varying delay systems is obtained in terms of LMIs. Numerical examples are given to verify the results by using matlab. When d = 0.3 and d is unknown,the results of this paper is less conservative than those in [11] and [15]. When d=0.1, compared with the literature [14], our resultis relatively conservative. But when d=0.3, d=0.5,d=0.8, compared with the literature [14], the proposed method can obtain better upper bounds of the time-delay. It is showed that the results of this paper have good advantages in comparison with the current methods when the bound of time delay derivative term is relatively large.