一类高阶矩阵差分方程的解及渐近稳定性  

The Solutions of a Class of High-order Matrix Difference Equations and Its Asymptotic Stability

作　　者：黄敬频[1] 许克佶 谭云龙[1] 黄杭州[1] 马陆陆[1] 

机构地区：[1]广西民族大学理学院,广西南宁530006

出　　处：《数学的实践与认识》2013年第24期258-262,共5页Mathematics in Practice and Theory

基　　金：广西高校科研项目(2013YB076);广西民族大学重点学科建设项目(2012SX)

摘　　要：讨论了一类高阶矩阵差分方程的解及渐近稳定性问题.利用特征子空间的维数得到了特征方程存在可对角化解的一个充要条件;然后利用特征方程的相异解刻划出该矩阵差分方程的通解,并给出其解渐近稳定的两个充分条件.推广了相关文献的结果.This paper is focused on the problem of the solutions of a class of high-order matrix difference equations and its asymptotic stability. By using dimensions of the eigen- subspaces, the necessary and sufficient conditions for the existence diagonalizable solutions of characteristic equation is obtained. Next, apply different solutions of characteristic equation, the general solution of the matrix difference equations is described. Meanwhile, two sufficient conditions its on asymptotic stability of the solution are given. The results extend some known conclusions in related literature.

关 键 词：矩阵差分方程 特征方程 通解 渐近稳定 

分 类 号：O175.7[理学—数学]