Time-Variant Systems and Interpolation

Inhaltsverzeichnis

• Nevanlinna-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.