Transfer functions of regular linear systems. III: Inversions and duality

DOI10.1007/s00020-002-1214-8zbMath1052.93032OpenAlexW2042080864MaRDI QIDQ1882523

George Weiss, Olof J. Staffans

Publication date: 1 October 2004

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-002-1214-8

zbMATH Keywords

transformationsconservative systemoperator semigroupregular linear systemwell-posed linear systemdual systemLax-Phillips semigroupflow-inversionsystem operatortime-flow-inversiontime-inversion

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Transformations (93B17) Operator-theoretic methods (93B28) Control/observation systems in abstract spaces (93C25) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items

Output Feedback Exponential Stabilization for One-Dimensional Unstable Wave Equations with Boundary Control Matched Disturbance ⋮ The Cayley Transform as a Time Discretization Scheme ⋮ Conservative boundary control systems ⋮ Representations and regularity of vector-valued right-shift invariant operators between half-line Bessel potential spaces ⋮ Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator ⋮ The H^∞-control problem for parabolic systems. Applications to systems with singular Hardy potentials ⋮ On evolution equations with white-noise boundary conditions ⋮ Well-posed state/signal systems in continuous time ⋮ Well-posed systems -- the LTI case and beyond ⋮ On perturbations of generators of \(C_0\)-semigroups ⋮ Time-varying additive perturbations of well-posed linear systems ⋮ Particular solution of infinite-dimensional linear systems with applications to trajectory planning of boundary control systems ⋮ Intermediate and extrapolated spaces for bi-continuous operator semigroups ⋮ Exact controllability of a class of nonlinear distributed parameter systems using back-and-forth iterations ⋮ How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance ⋮ On passive and conservative state/signal systems in continuous time ⋮ Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup ⋮ Spectral properties of infinite-dimensional closed-loop systems ⋮ When is a linear system conservative? ⋮ Spatial frequency range analysis for the nonlinear Schrödinger equation