A class of weakly regular Lp-well-posed linear systems. (May 2015) - Hamid, Bounit; Maragh, Fouad; Hammouri, Hassan
Abstract: We consider the weak regularity problem of L p -well-posed linear systems ( 1 ≤ p < ∞ ) in Banach state spaces when its associated unbounded controllers take values in the extrapolated Favard class. We prove that this type of L p -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] .