变系数线性系统谱的新不等式及其对部分变元稳定性的应用  

A New Spectral Inequality and Its Applications to Partial Stability of Linear Time-Varying Systems

作　　者：郭韵霞 

机构地区：[1]珠海广播电视大学数学系,广东珠海519000

出　　处：《应用数学》2007年第4期814-819,共6页Mathematica Applicata

摘　　要：本文利用一个非二次型李雅普诺夫函数,对变系数线性系统给出了一个新的谱不等式.不同于Wazewski不等式,我们避免了需要计算时变矩阵特征值的困难.然后我们利用新的谱不等式,讨论了变系数线性系统对部分变元的指数稳定性,得到了更实用的结果.In this paper, by using a non-quadratic Lyapunov function, we prove a new spectral inequality for linear time-varying systems with possibly unbounded coefficients. Unlike Wazewski＇s inequality,we do not require the calculation of eigenvalues for time-dependent matrices. The new spectral estimate is then applied to study the partial exponential stability problem of linear time-varying systems and several practical results are obtained.

关 键 词：变系数线性系统 谱估计 部分变元的稳定性 

分 类 号：O19[理学—数学]