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

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