Lyapunov, Bézout, and Hankel

DOI10.1016/0024-3795(84)90220-9zbMath0567.15008OpenAlexW1973131596MaRDI QIDQ1059692

Vlastimil Pták

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0024-3795(84)90220-9

zbMATH Keywords

companion matrixHankel matrixfactorizationmatrix equationsSchur-Cohn matrixBezoutian matricesLyapunov-type equationstruncated shift operator

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Matrix equations and identities (15A24)

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Cites Work

• Unnamed Item
• On the similarity transformation between a matrix and its transpose
• Bezoutians and projections
• An equation of Lyapunov type
• Zero location by Hermitian forms: the singular case
• On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem
• An elementary proof of the stability criterion of Lienard and Chipart
• Lyapunov equations and Gram matrices
• Analysis of the Lyapunov equation using generalized positive real matrices
• A generalization of the zero location theorem of Schur and Cohn
• Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations
• The discrete Lyapunov equation in controllable canonical form
• On another approach to the Schur-Cohn criterion
• A new proof of Hermite's stability criterion and a generalization of Orlando's formula
• On the solution of the discrete-time Lyapunov matrix equation in controllable canonical form
• Bigradients and the Problem of Routh and Hurwitz
• On the computation of the Cauchy index
• A Note on the Bezoutian Matrix