A gradient-based iterative algorithm for generalized coupled Sylvester matrix equations over generalized centro-symmetric matrices. (April 2014)

• Record Type: Journal Article
• Authors: Hajarian, Masoud
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 36:Number 2(2014)
• Page Start: 252
• Page End: 259
• Publication Date: 2014-04
• Subjects: Symmetric orthogonal matrix -- generalized centro-symmetric matrix -- iterative method -- the generalized coupled Sylvester matrix equations; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331213497499
• Languages: English
• ISSNs: 0142-3312

Abstract

Ann × n real matrixP is said to be a symmetric orthogonal matrix ifP = P − 1 = P T . Ann × n real matrixX is called a generalized centro-symmetric matrix with respect toP, ifX = PXP . It is obvious that everyn × n matrix is also a generalized centro-symmetric matrix with respect toI (identity matrix). In the present paper, we propose a gradient-based iterative algorithm to solve the generalized coupled Sylvester matrix equations { A 1 X 1 B 1 + C 1 X 2 D 1 = E 1, A 2 X 1 B 2 + C 2 X 2 D 2 = E 2, over the generalized centro-symmetric matrix pair( X 1, X 2 ) . It is proved that the iterative method is always convergent for any initial generalized centro-symmetric matrix pair( X 1 ( 1 ), X 2 ( 1 ) ) . Finally, a numerical example is discussed to illustrate the results.