Control, simulation and stability analysis of nonlinear regular proper DAEs

In this paper we provide an algorithm for nonlinear regular proper DAEs to derive a controller for an associated state space system assuming the algebraic variables and the error of the algebraic equations as fictitious inputs and outputs, respectively. It is shown that the achieved controlled state space representation has the same solution as the original DAE in the case of consistent initial values. Therefore, it can be used for stability analysis, designing control laws, and the numerical integration with standard methods. In contrast to the realization in minimal coordinates this formulation can be derived straight-forward and the computation is easy to implement on a computer algebra system.