Partial realization of descriptor systems

We address the partial realization problem for linear descriptor systems. A general solution to this problem using the Markov parameters of the system defined via its Laurent series is provided. For proper descriptor systems, we also discuss a numerically feasible algorithm for computing a partial minimal realization based on the unsymmetric Lanczos process. Applications to model reduction for two examples from computational fluid dynamics and mechanical systems with holonomic constraints are also given.