矩阵论在解线性定常系统状态方程中的应用  

Application of Matrix TheorySolving the Linear Fixed Constant System State Equations

作　　者：刘兆鹏[1] 李杰[1] LIU Zhaopeng;LI Jie(Colloge of Mathematics and Statistics,Institute of Suzhou,Suzhou,234000,China)

机构地区：[1]宿州学院数学与统计学院

出　　处：《吉林化工学院学报》2019年第11期81-85,共5页Journal of Jilin Institute of Chemical Technology

基　　金：安徽省教育厅科研项目(SK2018A0472);宿州学院科学研究重点项目(2019yzd17);宿州学院教研项目(szxy2018jyxm12)

摘　　要：讨论了线性定常系统的状态方程求解,得到了在特殊条件下,状态方程的求解方法.研究了线性定常系统状态方程的解在李雅普诺夫意义下的稳定性,得到了构造李雅普诺夫函数的新方法以及在一定条件下对线性定常连续系统和离散系统的李雅普诺夫方程的求解方法,该求解方法适合在计算机上编程运算.The paper discusses the state equation of regular linear systems and in special conditions the solution of the state equation is obtained.the paper analyzes the Lyapunov stability of the regular linear systems.Through the in-deep research on Lyapunov theorem a new method to construct Lyapunov function is found.The solution of the Lyapunov equation is very important too.The author finds a way to solve the Lyapunov equation of the continuous or discrete regular linear systems.This approach suits to make a program to solve the Lyapunov equation on the computer.

关 键 词：矩阵论 状态方程 李雅普诺夫方程 稳定性 

分 类 号：O151.2[理学—数学]