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Infinite-dimensional linear systems: a distributional approach

Published online by Cambridge University Press:  19 October 2005

Mark R. Opmeer
Mark R. Opmeer
Affiliation:
Mathematics Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. E-mail: [email protected]
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Abstract

We introduce the concept of a distributional resolvent linear system and solve the linear quadratic optimal control problem for this class of systems. The class of distributional resolvent linear systems includes all linear time-invariant systems that have been studied in the control literature.

We show connections with integrated semigroups and distribution semigroups and we consider some examples of systems described by partial differential equations that could not be handled by the existing theory.

Keywords

systems theorycontrolintegrated semigroupsdistribution semigroups47A4847D6249N1093C20
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 91 , Issue 3 , November 2005 , pp. 738 - 760
Copyright
2005 London Mathematical Society

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