A class of weakly regular Lp-well-posed linear systems. (May 2015)

• Record Type: Journal Article
• Authors: Hamid, Bounit; Maragh, Fouad; Hammouri, Hassan
• Is Part Of: European journal of control. Volume 23(2015:May)
• Page Start: 8
• Page End: 16
• Publication Date: 2015-05
• Subjects: Well-posed linear system -- Well-posed bilinear system -- Regular linear systems -- Regular bilinear systems -- Admissible operators -- Favard spaces; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2015.02.001
• Languages: English
• ISSNs: 0947-3580

Abstract

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] .