Analysis of over- and underdetermined nonlinear differential-algebraic systems with application to nonlinear control problems

We study over- and underdetermined systems of nonlinear differential-algebr aic equations. Such equations arise in many applications in circuit and mul tibody system simulation, in particular when automatic model generation is used, or in the analysis and solution of control problems in the behavior f ramework. We give a general (local) existence and uniqueness theory and apply the res ults to analyze when nonlinear implicit control problems can be made regula r by state or output feedback. The theoretical analysis also leads immediately to numerical methods for th e simulation as well as the construction of regularizing feedbacks.