On identification of stable systems and optimal approximation

Abstract Approximative modelling of stable continuous-time, possibly infinite dimensional, systems is studied based on an optimal approximation approach. Both approximation of analytical system representations (system approximation) as well as approximation of input-output data based system estimates (system identification) are considered. While special emphasis is given to approximative modelling in the H ∞ and Hankel norms, the L 1 and L 2 norm cases are also discussed. The model sets considered here are finite dimensional systems and time shifted systems (simple delay systems). The theory of approximation numbers is shown to provide a convenient tool to study problems of identification of stable continuous-time systems in a deterministic framework with close connections to complexity considerations. Laguerre-Fourier series methods and Hankel operator techniques can be utilized to develop fully practical identification methods for continuous-time, possibly infinite dimensional, systems.

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