caa a22 4500 606204903 CHVBK 20210128101004.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00034-014-9842-1 doi (NATIONALLICENCE)springer-10.1007/s00034-014-9842-1 Hajarian Masoud Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, 19839, Tehran, Iran aut A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations [Elektronische Daten] [Masoud Hajarian] 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. Springer Science+Business Media New York, 2014 Discrete-time periodic matrix equation nationallicence Iterative algorithm nationallicence Conjugate gradient method nationallicence Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/1(2015-01-01), 105-125 0278-081X 34:1<105 2015 34 34 https://doi.org/10.1007/s00034-014-9842-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9842-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hajarian Masoud Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, 19839, Tehran, Iran aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/1(2015-01-01), 105-125 0278-081X 34:1<105 2015 34 34