期刊
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
卷 36, 期 1, 页码 99-110出版社
SAGE PUBLICATIONS LTD
DOI: 10.1177/0142331213482485
关键词
Generalized Sylvester-transpose and conjugate matrix equation; iterative algorithm; reflexive (anti-reflexive) matrix
Linear matrix equations play an important role in many areas, such as control theory, system theory, stability theory and some other fields of pure and applied mathematics. In the present paper, we consider the generalized coupled Sylvester-transpose and conjugate matrix equations T-v(X) = F-v, v = 1, 2, ... , N, where X = (X-1,X-2, ... , X-p) is a group of unknown matrices and for v = 1,2, ... , N, T-v(X) = (p)Sigma(i=1) (s1)Sigma(mu=1) A(vi mu)X(i)B(vi mu) + (s2)Sigma(mu=1) (Cvi mu XiDvi mu)-D-T + (s3)Sigma(mu=1) M-vi mu(X) over bar N-i(vi mu) + (s4)Sigma(mu=1) H(vi mu)X(i)(H)G(vi mu,) in which A(vi mu), B-vi mu, C-vi mu, D-vi mu, M-vi mu, N-vi mu, H-vi mu, G(vi mu) and F-v are given matrices with suitable dimensions defined over complex number field. By using the hierarchical identification principle, an iterative algorithm is proposed for solving the above coupled linear matrix equations over the group of reflexive (anti-reflexive) matrices. Meanwhile, sufficient conditions are established which guarantee the convergence of the presented algorithm. Finally, some numerical examples are given to demonstrate the validity of our theoretical results and the efficiency of the algorithm for solving the mentioned coupled linear matrix equations.
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