Iterative-interpolation algorithms for L(2) model reduction

This paper is concerned with the construction of reduced–order models for high–order linear systems in such a way that the L2 norm of the impulse–response error is minimized. Two convergent algorithms that draw on previous procedures presented by the same authors, are suggested: one refers to s–domain representations, the other to time–domain state–space representations. The algorithms are based on an iterative scheme that, at any step, satisfies certain interpolation constraints deriving from the optimality conditions. To make the algorithms suitable to the reduction of very large–scale systems, resort is made to Krylov subspaces and Arnoldi’s method. The performance of the reduction algorithms is tested on two benchmark examples.