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主要讨论了一类退化时滞微分系统的稳定性问题.退化时滞微分系统稳定性的研究与非奇异系统或不带时滞的退化系统的稳定性研究均有不同.为了解决所遇到的困难,提出一种判定退化时滞微分系统稳定性的新判据.首先利用可逆的线性变换将系统转化为线性中立型微分系统,然后利用线性矩阵不等式以及构造Lyapunov函数,通过讨论这类线性中立型微分系统的渐近稳定性.进而获得退化时滞微分系统渐近稳定的条件。
The stability of a class of degenerate differential systems with time-delay is discussed in detail. The research on the stability of degenerate differential systems with time-delay is different from that of the non-singular systems or the degenerate systems without delay. We propose a new criterion to judge the stability of a retarded differential system.Firstly, the system is transformed into a linear neutral differential system by means of a reversible linear transformation. Then by using the linear matrix inequality and constructing Lyapunov functions, Asymptotic stability of the differential system and the asymptotic stability of the differential system with delay.