Systems theoretic aspects of PDAEs and applications to electrical circuits

The dissertation is about a systematic treatment of coupled systems of differential-algebraic and partial differential equations. Whereas in systems theory, differential-algebraic control systems lead to descriptor systems and controlled partial differential equations lead to infinite dimensional ordinary systems, the coupling of both requires a theory about descriptor systems with an infinite dimensional state space. Topics like solvability, decoupling, consistent initialization, perturbation analysis, Kaiman controllability/observability decomposition are treated for infinite dimensional descriptor systems. The theoretic results have been applied to a quite general class of delay-differential equations as weil as for electrical circuits with transmission lines. Moreover, several practical interpretations of the analytic aspects are given by means of the circuit topology.