中文摘要：

研究了带有双时变时滞的线性系统的稳定性问题。在过去线性系统的研究成果中,学者提出了大量的时滞系统的稳定性条件,这些稳定性条件都是旨在减小稳定系统的保守性。从减小稳定系统的保守性出发,改变稳定性条件,首次提出了一种不同寻常的不等式方法,即结合相互凸组合不等式和Park不等式方法,设计了新的系统稳定性条件,来减小线性放缩时系统产生的保守性。然后,在提出的新不等式方法和线性矩阵不等式的解决方法基础上,给出了保持系统稳定的判据。最后,通过数值仿真例子阐述了在相同系统的条件下,利用定理的方法得到的时滞相比于现存方法更大,验证了改进方法的有效性和可行性。

英文摘要：

This paper contributes to the study of stability of linear systems with two additive time-varying delays. In the case of linear systems, a lot of stability criteria have been proposed, whichall are aimed to reduce the conservatism of stability systems. However, seldom have the existingmethods contributed on the linear systems with two additive time-varying delays. In this paper, wefirst present an alternative inequality based on the reciprocally convex combination inequality andPark inequality. By designing an inequality technique, we can obtain a sufficient condition theoremand apply some existing methods to tractable LMI. Finally, time delay derivate by using ourtheorem is better than that of by using the existing ones under the same system. Numericalexamples are presented to demonstrate the improved method is effective and feasibly.