Efficient iterative solutions to general coupled matrix equations

Abstract

Linear matrix equations are encountered in many systems and control applications. In this paper, we consider the general coupled matrix equations (including the generalized coupled Sylvester matrix equations as a special case) Σ t=1lEtYtFt=Gs, s = 1, 2,..., l over the generalized reflexive matrix group (Y 1, Y 2,..., Y l). We derive an efficient gradient-iterative (GI) algorithm for finding the generalized reflexive solution group of the general coupled matrix equations. Convergence analysis indicates that the algorithm always converges to the generalized reflexive solution group for any initial generalized reflexive matrix group (Y 1(1), Y 2(1),..., Y l(1)). Finally, numerical results are presented to test and illustrate the performance of the algorithm in terms of convergence, accuracy as well as the efficiency. © 2013 Institute of Automation, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.