A note on POD model reduction methods for DAEs

We review some known results for proper orthogonal decomposition (POD) model order reduction applied to ordinary differential equations (ODEs). Then, these results are generalized for several types of differential-algebraic equations (DAEs). We provide algorithms for the model reduction and error bounds for the reduced-order models. Some limits of the approach are pointed out and alternative methods for reduced-order subspace approximation are presented. The POD approach is tested and evaluated for a medium-sized DAE example from multi-body dynamics.