Representation of infinite-dimensional neutral non-autonomous control systems

This paper studies the well-posedness of a class of non-autonomous neutral control systems in Banach spaces. We prove that such systems are represented by absolutely regular non-autonomous linear systems in the sense of Schnaubelt [R. Schnaubelt, Feedback for non-autonomous regular linear systems, SIAM J. Control Optim. 41 (2002) 1141–1165]. This paper can be considered as the non-autonomous version of the work presented in [H. Bounit, S. Hadd, Regular linear systems governed by neutral FDEs, J. Math. Anal. Appl. 320 (2006) 836–858].