基于SVD分解的二阶离散时变线性系统稳定性分析  

STABILITY ANALYSIS OF SECOND ORDER DISCRETE TIME-VARYING LINEAR SYSTEM BASED ON SVD DECOMPOSITION

作　　者：付波[1] 张行星 范秀香[1] 赵熙临[1] 何莉[1] Fu Bo;Zhang Xingxing;Fan Xiuxiang;Zhao Xilin;He Li(Hubei Key Laboratory for High-efficiency Utilization of Solar Energy and Operation Control of Energy Storage System,Hubei University of Technology,Wuhan 430068,Hubei,China)

机构地区：[1]湖北工业大学太阳能高效利用及储能运行控制湖北省重点实验室,湖北武汉430068

出　　处：《计算机应用与软件》2020年第12期37-45,共9页Computer Applications and Software

基　　金：国家自然科学基金项目(61072130,51309094,61603127);国家教育部留学回国人员科研启动基金项目(教外司留[2014]1685);湖北省科技厅重大专项(2013AEA001)。

摘　　要：连续系统的稳定性判据已经不适用于二阶离散时变线性系统,但目前仍未有较简便的稳定性判定方法。通过研究矩函数的三项递归式,并利用矩阵SVD分解将三项递归式所构成的二阶离散线性时变系统的状态方程转变为由一个旋转矩阵和一个对角矩阵构造的等效系统。根据李雅普诺夫理论得到几个二阶离散时变线性系统的稳定性判据和不稳定性判据。实验结果与所提出的判据相符合,验证了该判据的有效性。The stability criterion of continuous systems is not available to second order discrete time-varying linear system,but there is still no simple method for stability determination.This paper studies the three-term recursion of moment function,and uses the matrix SVD decomposition to transform the state equation of the second order discrete time-varying linear system into an equivalent system constructed by a rotation matrix and a diagonal matrix.According to Lyapunov theory,we obtain the stability criterion and instability criterion of second order discrete time-varying linear systems.The experimental results are consistent with the proposed criteria,which verify the effectiveness of the proposed criteria.

关 键 词：二阶离散时变线性系统 数值稳定性 SVD分解 三项递归公式 

分 类 号：TP311.52[自动化与计算机技术—计算机软件与理论]