On solutions to the matrix equations \(XB-AX=CY\) and \(XB-A\hat{X}=CY\)

DOI10.1016/j.jfranklin.2015.04.009zbMath1336.93068OpenAlexW253378649MaRDI QIDQ285675

Caiqin Song, Jun-E. Feng

Publication date: 19 May 2016

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2015.04.009

zbMATH Keywords

linear systemsstability analysiscontroller designblock diagonal matrix over complex fieldgeneralized Sylvester quaternion j-conjugate matrix equationgeneralized Sylvester real matrix equation

Mathematics Subject Classification ID

Design techniques (robust design, computer-aided design, etc.) (93B51) Linear systems in control theory (93C05) Stability of control systems (93D99)

Related Items (9)

A real representation of complex polynomial matrices in the framework of conjugate product ⋮ Solutions to matrix equations \(X - AXB = CY + R\) and \(X - A\hat{X}B = CY + R\) ⋮ A finite iterative algorithm for the general discrete-time periodic Sylvester matrix equations ⋮ New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation ⋮ Parametric solutions to generalized periodic Sylvester bimatrix equations ⋮ Convergence of HS version of BCR algorithm to solve the generalized Sylvester matrix equation over generalized reflexive matrices ⋮ Finite iterative solutions to periodic Sylvester matrix equations ⋮ Solutions to linear bimatrix equations with applications to pole assignment of complex-valued linear systems ⋮ Two modified least-squares iterative algorithms for the Lyapunov matrix equations

Cites Work

• Unnamed Item
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• Toward solution of matrix equation \(X=Af(X)B+C\)
• An explicit solution to the matrix equation \(AX - XF = BY\)
• On solutions of the matrix equations \(XF - AX = C\) and \(XF - A\bar {X} =C\)
• On solutions of matrix equations \(V - AVF = BW\) and \(V-A\bar V F= BW\)
• Ranks of a partitioned quaternion matrix under a pair of matrix equations
• On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)
• A Faddeev sequence method for solving Lyapunov and Sylvester equations
• On solutions of quaternion matrix equations \(XF-AX=BY\) and \(XF-A\widetilde{X}=BY\)
• On solutions of matrix equation \(XF-AX=C\) and \(XF-A\widetilde{X}=C\) over quaternion field
• Positive definite solutions of the nonlinear matrix equation \(X + A^H\bar{X}^{-1}A = I\)
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• The general solution to a system of real quaternion matrix equations
• On the solution of a Sylvester equation appearing in descriptor systems control theory
• On a solution of the quaternion matrix equation \(X-A \widetilde{X} B=C\) and its application
• Least squares solution of the quaternion matrix equation with the least norm
• Robust fault detection using Luenberger-type unknown input observers-a parametric approach
• A complete analytical solution to the equation<tex>TA - FT = LC</tex>and its applications
• New approach to robust observer design
• The Matrix Equation $A\bar X - XB = C$ and Its Special Cases
• Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control
• An eigenstructure assignment algorithm for the design of fault detection filters
• The quaternion matrix equation ΣA i XB i =E
• Quaternion-MUSIC for vector-sensor array processing
• Solutions of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems
• An algebraic relation between consimilarity and similarity of complex matrices and its applications
• Consimilarity of quaternion matrices and complex matrices

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