Trenn, Stephan - Distributional Differential Algebraic Equations

Universitätsverlag Ilmenau, Softcover, 189 Seiten

In this dissertation differential algebraic equations (DAEs) of the form Ex‘=Ax+f are studied. A main goal is the consideration of certain distributions (or generalized functions) as solutions and studying time-varying DAEs, whose coeffi cient matrices have jumps. Therefore, the space of piecewise-smooth distributions
is introduced as the solution space. For this space of distributions, it is possible to define a multiplication; hence, DAEs can be studied whose coefficient matrices have also distributional entries. Necessary and sufficient conditions for existence and uniqueness of (distributional) solutions are derived. For switched DAEs, sufficient conditions are given which ensure that all solutions are impulse free and stability is studied. Finally, controllability and observability are defined for distributional DAEs. A normal form for time-invariant pure DAEs is derived which allows for a simple characterization of controllability and observability.