Paper Info
Title
A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations
Abstract
Analysis and design of linear periodic control systems are closely related to the discrete-time periodic matrix equations. In this paper, we propose an iterative algorithm based on the conjugate gradient method on the normal equations (CGNE) for finding the solution group of the general coupled periodic matrix equations $$\\begin{aligned} \\left\\{ \\begin{array}{l} A_{1,i}X_iB_{1,i}+C_{1,i}X_{i+1}D_{1,i}=E_{1,i},\\\\ A_{2,i}X_iB_{2,i}+C_{2,i}X_{i+1}D_{2,i}=E_{2,i}, \\end{array} \\right. ~~~\\mathrm {for}~~~i=1,2,3,\\ldots . \\end{aligned}$$ A 1 , i X i B 1 , i + C 1 , i X i + 1 D 1 , i = E 1 , i , A 2 , i X i B 2 , i + C 2 , i X i + 1 D 2 , i = E 2 , i , for i = 1 , 2 , 3 , ¿ . By proving some properties of the algorithm, we show that the solution group of the periodic matrix equations can be obtained within a finite number of iterations in the absence of roundoff errors. Numerical examples are given to illustrate the efficiency and accuracy of the proposed algorithm.
Year
DOI
Venue
2015
10.1007/s00034-014-9842-1
CSSP
Keywords
Field
DocType
Discrete-time periodic matrix equation, Iterative algorithm, Conjugate gradient method
Conjugate gradient method,Discrete mathematics,Mathematical optimization,Finite set,Matrix (mathematics),Iterative method,Discrete time and continuous time,Periodic graph (geometry),Mathematics
Journal
Volume
Issue
ISSN
34
1
1531-5878
Citations 
PageRank 
References 
5
0.42
14
Authors
1
Name
Order
Citations
PageRank
Masoud Hajarian134524.18