A semigroup characterization of well-posed linear control systems

Abstract

We study the well-posedness of a linear control system $\Sigma (A,B,C,D)$ with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space ${\mathcal{X}}^p$ and call it $p$-well-posed if $\mathcal{A}$ generates a strongly continuous semigroup on ${\mathcal{X}}^p$. Our approach is based on the Laplace transform and Fourier multipliers.