Stability analysis of systems with two additive time-varying delay components via an improved delay interconnection Lyapunov-Krasovskii functional
Stability analysis of systems with two additive time-varying delay components via an improved delay interconnection Lyapunov-Krasovskii functional
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DOI：
10.1016/j.jfranklin.2019.02.006
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
Meng Liu;Yong He;Min Wu;Jianhua Shen
中科院分区：
文献类型：
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作者：
Meng Liu;Yong He;Min Wu;Jianhua Shen
本文在改进的时滞关联Lyapunov-Krasovskii框架下研究了具有两个附加时变时滞分量的系统的稳定性。首先，在Lyapunov-Krasovskii泛函（LKF）中引入一个增广向量和一些积分项，以新的方式考虑了附加时延信息，充分考虑了两个上界的信息以及这两个上界与总时延上界之间的关系。然后，所得到的稳定性准则显示出优于现有的，因为不仅构造了一个改进的延迟互连LKF，而且还使用了一些先进的技术，如基于自由矩阵的积分不等式和扩展的凸矩阵不等式估计的导数的上界建议LKF。最后，通过数值算例验证了该方法的有效性，并显示了其优于已有结果的优越性。
This paper is concerned with the stability analysis of systems with two additive time-varying delay components in an improved delay interconnection Lyapunov–Krasovskii framework. At first, an augmented vector and some integral terms considering the additive delays information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF), in which the information of the two upper bounds and the relationship between the two upper bounds and the upper bound of the total delay are both fully considered. Then, the obtained stability criterion shows advantage over the existing ones since not only an improved delay interconnection LKF is constructed but also some advanced techniques such as the free-matrix-based integral inequality and extended reciprocally convex matrix inequality are used to estimate the upper bound of the derivative of the proposed LKF. Finally, a numerical example is given to demonstrate the effectiveness and to show the superiority of the proposed method over existing results.