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distribution semigroups

Proceedings of the London Mathematical Society (1)

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Infinite-dimensional linear systems: a distributional approach
Mark R. Opmeer
Journal:

Proceedings of the London Mathematical Society / Volume 91 / Issue 3 / November 2005

Published online by Cambridge University Press:

19 October 2005, pp. 738-760

Print publication:

November 2005
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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.