Closed-form solutions to the nonhomogeneous Yakubovich-conjugate matrix equation

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Original languageEnglish
Pages (from-to)442-450
Journal / PublicationApplied Mathematics and Computation
Issue number2
Publication statusPublished - 15 Aug 2009


Some closed-form solutions are provided for the nonhomogeneous Yakubovich-conjugate matrix equation X - A over(X, -) F = 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. © 2009 Elsevier Inc. All rights reserved.

Research Area(s)

  • Closed-form solution, Controllability matrix, Observability matrix, Parametric expression, Smith normal form, Yakubovich-conjugate matrix equation

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