Toda flows, inverse spectral transform and realization theory

DOI10.1016/0167-6911(91)90001-UzbMath0734.93032OpenAlexW4231939357MaRDI QIDQ811465

Roger W. Brockett, Leonid Faybusovich

Publication date: 1991

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6911(91)90001-u

zbMATH Keywords

realization theorycompletely integrable nonlinear differential equationsToda-like completely integrable systems

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Control/observation systems in abstract spaces (93C25) Realizations from input-output data (93B15)

Related Items (9)

Rational functions, Toda flows, and LR-like algorithms ⋮ Lie algebraic aspects of the finite nonperiodic Toda flows ⋮ Tangent spaces of rational matrix functions ⋮ Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective ⋮ The finite discrete KP hierarchy and the rational functions ⋮ Elementary Toda orbits and integrable lattices ⋮ Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices ⋮ Asymptotic Hamiltonian dynamics: The Toda lattice, the three-wave interaction and the non-holonomic Chaplygin sleigh ⋮ Hamiltonian and gradient structures in the Toda flows

Cites Work

• Unnamed Item
• Unnamed Item
• A cell decomposition of the space of real Hankel matrices of rank \(\leq n\) and some applications
• On the partial realization problem
• Nahm's equations and the classification of monopoles
• Self-similar flows
• QR-type factorizations, the Yang-Baxter equation, and an eigenvalue problem of control theory
• A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map
• A scaling theory for linear systems
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Some geometric questions in the theory of linear systems

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