A class of weakly regular Lp-well-posed linear systems

We consider the weak regularity problem of Lp-well-posed linear systems (1≤p<∞)(1≤p<∞) in Banach state spaces when its associated unbounded controllers take values in the extrapolated Favard class. We prove that this type of Lp-well-posed linear systems are weakly regular, and this regularity is output operators independent up to the well-posedness, provided that the adjoint of the underlying semigroups is strongly continuous on its dual. We present some applications of our results to a class of boundary control systems and a class of well-posed bilinear systems recently introduced in [2].