一个推广的矩阵李亚普诺夫函数及其应用

A Generalized Lyapunov Matrix-Function and its Applications

1984年,Martynyuk提出了矩阵李亚普诺夫函数的概念并研究了它在稳定性理论中的应用。但在他的文中有很多不足之处。本文提出一个形式上比Martynyuk更广泛的矩阵李亚普诺夫函数,它包含标量、向量李亚普诺夫函数。

In 1984, Martynyuk [1,2] proposed a concept of Lyapunov matrix-functionand researched its application in the theory of stsbility. Martynyuk's idea is very interesting;however, there exists some shortcoming in his papers. In the present paper, we proposed ageneralized Lyapunov matrix-function and studied its properties, by using this function.we studied its application in the theory of stability, and got some succinct results, which canbe regarded as the progress to Martynyuk's main results in his papers.