An iterative algorithm to solve the generalized coupled Sylvester-transpose matrix equations. (July 2016)

• Record Type: Journal Article
• Authors: Song, Caiqin; Feng, Jun-e
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 38:Number 7(2016)
• Page Start: 863
• Page End: 875
• Publication Date: 2016-07
• Subjects: coupled Sylvester-transpose matrix equations -- least Frobenius norm generalized centro-symmetric solution -- iterative algorithm -- optimal approximation generalized centro-symmetric solution; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331215588808
• Languages: English
• ISSNs: 0142-3312

Abstract

This note presents an iterative algorithm to solve the coupled Sylvester-transpose matrix equations (including the generalized coupled Sylvester matrix equations and Lyapunov matrix equations as special cases) over generalized centro-symmetric matrices. When the considered matrix equations are consistent, for any initial generalized centro-symmetric matrix group, a generalized centro-symmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors. The least Frobenius norm generalized centro-symmetric solution group of the coupled Sylvester-transpose matrix equations can be derived when a suitable initial generalized centro-symmetric matrix group is chosen. In addition, for a given generalized centro-symmetric matrix group, the optimal approximation generalized centro-symmetric solution group can be obtained by finding the least Frobenius norm generalized centro-symmetric solution group of new coupled Sylvester-transpose matrix equations. Finally, a numerical example is given to demonstrate the efficiency of the introduced iterative algorithm.