Hankel model reduction without balancing-A descriptor approach

A basis-free descriptor system representation is shown to facilitate the computation of all minimum-degree and optimal kth order all-pass extensions and Hankel-norm approximates. The descriptor representation has the same simple form for both the optimal and for the suboptimal minimunl degree cases. The method eliminates the need for the potentially ill-conditioned calculation of a minimal balanced, or partially balanced, realization of the system to be reduced. A simple, numerically sound method based on singular-value decomposition enables the results to be expressed in state-space form. A listing of PC-MATLAB code which implements the algorithm can be found in authors´ program LINF.