A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations

摘要

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 $$begin{aligned} left{ begin{array}{l} A_{1,i}X_iB_{1,i}+C_{1,i}X_{i+1}D_{1,i}=E_{1,i}, A_{2,i}X_iB_{2,i}+C_{2,i}X_{i+1}D_{2,i}=E_{2,i}, end{array} right. ~~~mathrm {for}~~~i=1,2,3,ldots . end{aligned}$$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. Keywords Discrete-time periodic matrix equation Iterative algorithm Conjugate gradient method Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (35) References1.P. Benner, M.S. Hossain, Structure Preserving Iterative Solution of Periodic Projected Lyapunov Equations, in Proceedings of MATHMOD conference, Vienna 20122.P. Benner, M.S. Hossain, T. Stykel, Low rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems (Chemnitz Scientific Computing Preprints, 2011)3.P. Benner, M.S. Hossain, T. 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Inform. 9, 337–345 (2013)CrossRef About this Article Title A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix Equations Journal Circuits, Systems, and Signal Processing Volume 34, Issue 1 , pp 105-125 Cover Date2015-01 DOI 10.1007/s00034-014-9842-1 Print ISSN 0278-081X Online ISSN 1531-5878 Publisher Springer US Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Circuits and Systems Electrical Engineering Signal, Image and Speech Processing Electronics and Microelectronics, Instrumentation Keywords Discrete-time periodic matrix equation Iterative algorithm Conjugate gradient method Industry Sectors Automotive Electronics IT & Software Telecommunications Aerospace Oil, Gas & Geosciences Engineering Authors Masoud Hajarian (1) Author Affiliations 1. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, 19839 , Tehran, Iran Continue reading... To view the rest of this content please follow the download PDF link above.