On the Regularity for Some Class

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