Using Feedback to Improve System Identification

Abstract

In his Doctoral thesis and subsequent publications (e.g., [1]) Keith Glover explored the parameterization of multivariable time invariant linear systems investigating identifiability and suitable standard forms for use in system identification. Over the years the idea of identifiability has come to play an important role in the literature. In this paper we describe some new results centering around a quantitative measure of identifiability defined in terms of a suitable Gramian. The motivation comes from a desire to provide a quantitative evaluation of the so-called “two dimensional method” widely used in nuclear magnetic resonance (NMR) spectroscopy and we provide this in terms of a Cramer-Rao bound. In the final section we expand the scope of these ideas, providing a more general system theoretic development which discusses a new role for feedback in system identification.