Feedback theory for neutral equations in infinite dimensional state spaces

Abstract

This paper is concerned with neutral partial differential equations with atomic difference operators in infinite dimensional state Hilbert spaces. Here we introduce an approach based essentially on representation of closed loop systems of well-posed and regular linear systems in Salamon-Weiss sense. This technique allows us to introduce a new formulation of generalized solutions of such equations. Furthermore we study spectral theory and positivity of the semigroup solution.