一类由偏微分方程描述的大型动力系统的稳定性(英文)

THE STABILITY OF A CLASS OF LARGE SCALE SYSTEMS DESCRIBED BY PARTIAL DIFFERENTIAL EQUTIONS

本文研究了一类由偏微分方程描述的大型动力系统的稳定性问题,利用分解方法给出了大系统的解渐近稳定的代数条件,并将结果推广到了非线性情形;此外还讨论了一般偏微允方程描述的大系统的稳定性,给出了大系统稳定的充分条件。为实际工作者提供了一种实用的稳定性分析方法。

In this paper, the stability of a class of large scale dynamic systems described by partial differential equations is investigated by means of the decomposition method. Firstly, the conditions of asymptotic stability for large scale systems are obtained, and the result is also generalized to nonlinear systems. Secondly, the stability of large scale systems described by general partial differential equations is also discussed, and the conditions of stability are given. The results given in this paper provide an effective analysis approach of stability for applications.