线性时变系统的若干问题

Some Problems of Linear Time-Varying Systems

线性时变系统由于状态转移矩阵Ф（ｔ，ｔ０）的特性一般不能由系统矩阵的Ａ（ｔ）的特征值来表征，确定时变系统的稳定性是十分困难的。讨论了线性时变系统能控性的两个必要条件及其能稳定性的一个充分条件。在研究时变系统中利用定常系统的方法有效地解决了一些问题，为进一步研究时变系统做了一种尝试，具有一定实际意义。

Because characters of linear time-varying systems state transfer function matrix Φ(t,t 0) can not be expressed by the eigenvalues of system matrix A(t) generally, the time-varying stability is diffcult to be found. The two controllable necessary conditions and a sufficient condition of stability of linear time-varying systems are discussed. The problems of time-varying systems are discussed by using the time-nonvarying systems method. This method dissvoles some problems effectively.