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## Frequency Domain Methods and Decoupling of Linear Constant Coefficient Infinite Dimensional Differential Algebraic Systems

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Author(s) : Timo Reis , Caren Tischendorf

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 01-2005

MSC 2000

34A09 Implicit equations, differential-algebraic equations
34A30 Linear equations and systems, general

Abstract :
We discuss the analysis of constant coefficient linear differential algebraic equations $E\dot{x}(t)=Ax(t)+q(t)$ on infinite dimensional Hilbert spaces. We give solvability criteria of these systems which are mainly based on Laplace transformation. Furthermore, we investigate decoupling of these systems, motivated by the decoupling of finite dimensional differential algebraic systems by the Kronecker normal form. Applications are given by the analysis of mixed systems of ordinary differential, partial differential and differential algebraic equations.

Keywords : partial differential-algebraic equations, index, infinite dimensional linear system theory