An explicit solution to the matrix equation \(AX - XF = BY\)

DOI10.1016/j.laa.2005.01.018zbMath1076.15016OpenAlexW2155848675MaRDI QIDQ556908

Bin Zhou, Guang-Ren Duan

Publication date: 23 June 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.01.018

zbMATH Keywords

pole assignmentfeedbackLyapunov equationHankel matrixgeneralized Sylvester matrix equationcontrollability matrixobservability matrixparametrized solution

Mathematics Subject Classification ID

Controllability (93B05) Feedback control (93B52) Pole and zero placement problems (93B55) Matrix equations and identities (15A24) Observability (93B07)

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Cites Work

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• Controllability, observability and the solution of AX-XB=C
• Pole assignment via Sylvester's equation
• Solution to matrix equation \(AV + BW = EVF\) and eigenstructure assignment for descriptor systems
• Nonsingular solutions of TA-BT=C
• A complete analytical solution to the equation&lt;tex&gt;TA - FT = LC&lt;/tex&gt;and its applications
• Solution of Lyapunov equation with system matrix in companion form
• On the solution to the Sylvester matrix equation AV+BW=EVF
• Solutions of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems
• Resultants and the Solution of $AX - XB = - C$

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