Journal
SYSTEMS & CONTROL LETTERS
Volume 54, Issue 2, Pages 95-107Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.sysconle.2004.06.008
Keywords
Sylvester matrix equation; Lyapunov matrix equation; identification; estimation; least squares; Jacobi iteration; Gauss-Seidel iteration; Hadamard product; star product; hierarchical identification principle
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In this paper, we present a general family of iterative methods to solve linear equations, which includes the well-known Jacobi and Gauss-Seidel iterations as its special cases. The methods are extended to solve coupled Sylvester matrix equations. In our approach, we regard the unknown matrices to be solved as the system parameters to be identified, and propose a least-squares iterative algorithm by applying a hierarchical identification principle and by introducing the block-matrix inner product (the star product for short). We prove that the iterative solution consistently converges to the exact solution for any initial value. The algorithms proposed require less storage capacity than the existing numerical ones. Finally, the algorithms are tested on computer and the results verify the theoretical findings. (C) 2004 Elsevier B.V. All rights reserved.
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