一类Lyapunov矩阵方程组的迭代方法  

An iterative method for solving coupled Lyapunov equations

作　　者：丁振亚[1] 段雪峰[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2012年第5期421-425,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11101100);广西自然科学基金(2012GXNSFBA053006)

摘　　要：为了得到一种有效的算法来求解离散马尔科夫跳跃线性系统中出现的Lyapunov矩阵方程组,基于递阶辨识原理和梯度迭代算法,构造了一种新的迭代算法。该算法利用递阶辨识原理将原本复杂的Lyapunov矩阵方程组简单化,使其更易于求解,并给出了2个数值例子。理论研究和数值实验表明,此算法是行之有效的,且具有一定的应用价值。In order to get a effective algorithm to solve the Lyapunov matrix equations in the discrete-time Markovian jump linear system.A new iterative algorithm based on the hierarchical identification principle and the gradient algorithm was constructed.The algorithm used the hierarchical identification principle that let the complex Lyapunov matrix equations into a simple equations,so as to make it easier to solve.Finally,two numerical examples was given.Theory and numerical experiments show that this algorithm is effective and has application value.

关 键 词：Lyapunov矩阵方程组 迭代算法 收敛性 离散马尔科夫跳跃线性系统 

分 类 号：O241.6[理学—计算数学]