Gradient Based Iterative Algorithm to Solve General Coupled DiscreteTime Periodic Matrix Equations over Generalized Reflexive Matrices
Gradient Based Iterative Algorithm to Solve General Coupled DiscreteTime Periodic Matrix Equations over Generalized Reflexive Matrices
复制标题
DOI：
10.3846/13926292.2016.1186119
复制
发表时间：
2016-06
影响因子：
1.8
通讯作者：
M. Hajarian
中科院分区：
文献类型：
--
作者：
M. Hajarian
摘要 在周期状态反馈问题和周期描述符系统的模型简化中会遇到离散时间周期矩阵方程。本文的目的是计算一般耦合离散时间周期矩阵方程的广义自反解。我们引入了一种基于梯度的迭代（GI）算法，用于寻找一般耦合离散时间周期矩阵方程的广义自反解。结果表明，对于任何初始广义自反矩阵，所引入的 GI 算法总是收敛于广义自反解。最后，通过两个数值例子来验证 GI 算法的效率。
AbstractThe discretetime periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. We introduce a gradientbased iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discrete time periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm.