Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 214, Issue 2, Pages 442-450Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2009.04.011
Keywords
Yakubovich-conjugate matrix equation; Closed-form solution; Parametric expression; Controllability matrix; Observability matrix; Smith normal form
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Some closed-form solutions are provided for the nonhomogeneous Yakubovich-conjugate matrix equation X - A (X) over barF = BY + R with X and Y being unknown matrices. The presented solutions can offer all the degrees of freedom which is represented by an arbitrarily chosen parameter matrix. The primary feature of the solutions is that the matrices F and R are not restricted to be in any canonical form, or may be even unknown a priori. One of the solutions is neatly expressed in terms of controllability matrices and observability matrices. (C) 2009 Elsevier Inc. All rights reserved.
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