31 May 1996 Nevanlinna-Pick interpolation and robust control for time-varying systems
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Abstract
For the case of linear, time-invariant, finite-dimensional systems, the connection between the so-called standard problem of H(infinity ) control and classical Nevanlinna-Pick interpolation is now well known. Indeed H(infinity )-admissible closed loop transfer functions (i.e. those closed-loop transfer functions corresponding to compensators which guarantee internal stability of the closed loop system for a given open loop plant) can be characterized as all stable transfer functions which in addition satisfy a collection of interpolation conditions (explicitly computable from the original open loop plant). Not so well known is that this frequency domain-type approach, when interpreted operator theoretically in the time domain, extends mutatis mutandis to time-varying systems as well. In this short note we review the standard problem of H(infinity )-control and its connection with robust stabilization, sketch how the standard solution can be recovered as the solution of a matrix Nevanlinna-Pick interpolation problem, and indicate how the ideas (including a notion of point evaluation and frequency response function) generalize to the time-varying case.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Joseph A. Ball, "Nevanlinna-Pick interpolation and robust control for time-varying systems", Proc. SPIE 2715, Smart Structures and Materials 1996: Mathematics and Control in Smart Structures, (31 May 1996); doi: 10.1117/12.240849; https://doi.org/10.1117/12.240849
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