A Faddeev sequence method for solving Lyapunov and Sylvester equations

DOI10.1016/0024-3795(95)00683-4zbMath0859.65038OpenAlexW2073038832MaRDI QIDQ1923160

Ralf L. M. Peeters, Bernard Hanzon

Publication date: 25 March 1997

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00683-4

zbMATH Keywords

Lyapunov matrix equationdirect methodsmatrix inversionSylvester matrix equationFaddeev methodFaddeev sequence

Mathematics Subject Classification ID

Related Items (25)

Solutions to the linear transpose matrix equations and their application in control ⋮ On solutions to the matrix equations \(XB-AX=CY\) and \(XB-A\hat{X}=CY\) ⋮ Closed-form solutions to the nonhomogeneous Yakubovich-conjugate matrix equation ⋮ Algorithms for finding the minimal polynomials and inverses of resultant matrices ⋮ Detection of Energy Balance Anomalies in the Bilinear Dynamic Systems ⋮ Computational Methods for Linear Matrix Equations ⋮ On matrix equations \(X - AXF = C\) and \(X - A\overline{X}F = C\) ⋮ On the methods for calculation of Gramians and their use in analysis of linear dynamic systems ⋮ On solutions of the matrix equations \(XF - AX = C\) and \(XF - A\bar {X} =C\) ⋮ Closed-form solutions to Sylvester-conjugate matrix equations ⋮ On computational methods for Gramians of continuous dynamic systems ⋮ On properties of gramians of continuous control systems ⋮ Iterative solutions to the Kalman-Yakubovich-conjugate matrix equation ⋮ Spectral decompositions of Gramians and energy metrics of continuous unstable control systems ⋮ A real representation method for solving Yakubovich-\(j\)-conjugate quaternion matrix equation ⋮ Optimal adaptive design of the prescribed-structure controllers ⋮ Explicit solutions to the quaternion matrix equationsX−AXF=CandX−A[XtildeF=C] ⋮ On solutions of matrix equations \(V - AVF = BW\) and \(V-A\bar V F= BW\) ⋮ On solutions of matrix equation \(XF-AX=C\) and \(XF-A\widetilde{X}=C\) over quaternion field ⋮ Stability analysis of large‐scale dynamical systems by sub‐Gramian approach ⋮ On the explicit solutions of forms of the Sylvester and the Yakubovich matrix equations ⋮ A two-variable approach to solve the polynomial Lyapunov equation ⋮ Convex invertible cones of matrices -- a unified framework for the equations of Sylvester, Lyapunov and Riccati ⋮ The Fisher information matrix for linear systems. ⋮ Finite algorithms for solving the coupled Sylvester-conjugate matrix equations over reflexive and Hermitian reflexive matrices

Cites Work

• Factored forms for solutions of \(AX-XB=C\) and \(X-AXB=C\) in companion matrices
• Fast projection methods for minimal design problems in linear system theory
• Balanced realizations: canonical form, parametrization, model reduction
• Formulae for the solution of Lyapunov matrix equations
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