一类滞后型时变广义系统解的稳定性

Stability of Solutions of a Class of Time-varying Singular Systems with Delay

滞后广义系统解的稳定性的研究与非奇异系统或不带滞后的广义系统解的稳定性研究均有不同。为了解决所遇到的新困难,一种稳定性的新概念被提出,同时,通过Lyapunov函数方法,两个稳定性判定定理得以建立。这些结果被应用于线性系统,得到了一个关于线性系统稳定性判定的很有价值的结果。

There are some differences between the discussion of stability of singular systems with delay and that of stability of nonsingular systems or singular systems without delay. In order to overcome the encoun-tered new difficulties , a new definition of stability of soultions of singular systems with delay was introduced in this paper. Then two theorems on stability were established by Lyapunov function. At last, these theo-rems were applied into the discussion of linear autonomous singular systems with delay and a valuable theo-rem for judgment of stability of solutions of this kind of systems was obtained.