Time-Variant Systems and Interpolation

InhaltsverzeichnisNevanlinna-Pick interpolation for time-varying input-output maps: The discrete case.0. Introduction.1. Preliminaries.2. J-Unitary operators on ?2.3. Time-varying Nevanlinna-Pick interpolation.4. Solution of the time-varying tangential Nevanlinna-Pick interpolation problem.5. An illustrative example.References.Nevanlinna-Pick interpolation for time-varying input-output maps: The continuous time case.1. Generalized point evaluation.2. Bounded input-output maps.3. Residue calculus and diagonal expansion.4. J-unitary and J-inner operators.5. Time-varying Nevanlinna-Pick interpolation.6. An example.Dichotomy of systems and invertibility of linear ordinary differential operators.1. Introduction.2. Preliminaries.3. Invertibility of differential operators on the real line.4. Relations between operators on the full line and half line.5. Fredholm properties of differential operators on a half line.6. Fredholm properties of differential operators on a full line.7. Exponentially dichotomous operators.8. References.Inertia theorems for block weighted shifts and applications.2. One sided block weighted shifts.3. Dichotomies for left systems and two sided systems.4. Two sided block weighted shifts.5. Asymptotic inertia.6. References.Interpolation for upper triangular operators.3. Colligations & characteristic functions.4. Towards interpolation.5. Explicit formulas for ?.6. Admissibility and more on general interpolation.7. Nevanlinna-Pick Interpolation.8. Carathéodory-Fejér interpolation.9. Mixed interpolation problems.10. Examples.11. Block Toeplitz & some implications.12. Varying coordinate spaces.13. References.Minimality and realization of discrete time-varying systems.2. Observability and reachability.3. Minimality for time-varying systems.4. Proofs of the minimality theorems.5. Realizations of infinite lower triangular matrices.6. The class of systems with constant state space dimension.7. Minimality and realization for periodical systems.