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

We discuss the analysis of linear constant coefficient differential algebraic equations on infinite dimensional Hilbert spaces. We give solution concepts and discuss solvability criteria which are mainly based on Laplace transform. Furthermore, we investigate the decoupling of these systems motivated by the Kronecker normal form for the finite dimensional case. Applications are given by the analysis of mixed systems of ordinary differential, partial differential and differential algebraic equations.