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 numerically feasible algorithms for computing a partial minimal realization based on the unsymmetric Lanczos and Arnoldi processes. Applications to model reduction for examples from computational fluid dynamics and mechanical systems with holonomic constraints are also given.