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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.

DOI Code: 10.1285/i15900932v28n1p43

Keywords: translation semigroup; neutral equations; regular linear systems; feedback

Classification: 47D06; 34K40; 93C05; 93B52

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