A Geometric Approach to System Identification Using Model-reduction Techniques

Abstract

The geometry of the space of all stable linear systems of order smaller than or equal to n is important in system identification, especially in recursive identification. To construct (generalized) gradient algorithms that are independent of the parametrization of the space, one needs to specify a metric on each tangent space. A general method to obtain such metrics is to embed the set of all stable linear systems of order smaller than or equal to n in the set of all stable linear systems (with given input and output dimensions) and to specify a metric there. Under certain conditions this induces a metric on each tangent space. In the theory of model reduction there is one metric that has led to some very nice results, namely the metric that derives from the Hankel norm. In this paper the geometry is investigated that results if one uses the Hankel norm as a starting point. It is a so-called Finsler geometry.