Time-Variant Systems and Interpolation

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The annotation covers various topics related to Nevanlinna-Pick interpolation for time-varying input-output maps in both discrete and continuous cases. It begins with an introduction and preliminaries, followed by discussions on J-unitary operators, generalized point evaluation, and bounded input-output maps. The text delves into the solution of the time-varying tangential interpolation problem, providing illustrative examples and references. Additionally, the work addresses the dichotomy of systems and the invertibility of linear ordinary differential operators, exploring their properties on both the real line and half line, as well as Fredholm properties and exponentially dichotomous operators. It further examines inertia theorems for block weighted shifts, detailing one-sided and two-sided systems, asymptotic inertia, and related references. The interpolation for upper triangular operators is also discussed, including colligations, characteristic functions, explicit formulas, admissibility, and various interpolation methods such as Nevanlinna-Pick and Carathéodory-Fejér interpolation, along with mixed interpolation problems and examples. Lastly, the text addresses minimality and realization of discrete time-varying systems, focusing on observability, reachability, proofs of minimality theorems, realizations of infinite lower triangular matrices, and systems with constant state space dimension, including periodical system