We study the well-posedness of a linear control system Σ(A,B,C,D) with unbounded control and observation operators. To this end we associate to our system an operator matrix A on a product space X^p and call it p-well-posed if A generates a strongly continuous semigroup on X^p. Our approach is based on the Laplace transform and Fourier multipliers. The results generalize and complement those of [4], [25] and are illustrated by a heat equation with boundary control and point observation.
A Semigroup Characterization of Well-Posed Linear Control Systems
ENGEL, KLAUS JOCHEN OTTO;
2014-01-01
Abstract
We study the well-posedness of a linear control system Σ(A,B,C,D) with unbounded control and observation operators. To this end we associate to our system an operator matrix A on a product space X^p and call it p-well-posed if A generates a strongly continuous semigroup on X^p. Our approach is based on the Laplace transform and Fourier multipliers. The results generalize and complement those of [4], [25] and are illustrated by a heat equation with boundary control and point observation.File in questo prodotto:
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