Firstly, we give some technologies and notations, and introduce the definitions of numerical range , convex set, extreme point, maximal partial isometry etc. Subsequently we give some well-known theorems such as the Krein-Milman theorem, polar decomposition theorem and spectral theorem.
首先我们介绍了一些符号的表示意义,接着引入了数值域,凸集,凸集端点,极大部分等距等概念,而后给出一些广泛熟知的定理如Krein-Milman定理,极分解定理,谱定理等。
Based on Lyapunov stability theory, Razumikhin stability theory and convex set theory, linear matrix inequality, matrix analyzing methods and convex programming are adopted in this paper.
本文的研究工作主要基于Lyapunov稳定性定理,Razumikhin稳定性定理以及凸集的有关理论,并采用了线性矩阵不等式,矩阵分析以及凸规划等工具。