Summary
In this expository paper we provide an overview of recent developments in realization theory and system identification for the class of rational systems. Rational systems are a sufficiently big class of systems to model various phenomena in engineering, physics, economy, and biology which still has a nice algebraic structure. By an algebraic approach we derive necessary and sufficient conditions for a response map to be realizable by a rational system. Further we characterize identifiability properties of rational systems with parameters. For the proofs we refer the reader to the corresponding papers.
This paper is dedicated to Christopher I. Byrnes and to Anders Lindquist for their contributions to control and system theory.
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Němcová, J., van Schuppen, J.H. (2010). Rational Systems – Realization and Identification. In: Hu, X., Jonsson, U., Wahlberg, B., Ghosh, B. (eds) Three Decades of Progress in Control Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11278-2_22
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