Systems & Control Letters Volume 8, Issue 3 , January 1987, Pages 197-204

How exciting can a signal really be?

I. M. Y. Mareels * , R. R. Bitmead, M. Gevers, C. R. Johnson, Jr ** , R. L. Kosut b ^{,
^a} and M. A. Poubelle

Department of Systems Engineering, Research of Physical Sciences, P.O. Box 4, Australian National University, Canberra, A.C.T. 2601, Australia School of Electrical Engineering, Cornell University, Ithaca, NY, USA ^a Integrated Systems Inc., Palo Alto, CA, USA ^b Department of Electrical Engineering, Stanford University, Stanford, CA, USA Turramurra Institute of Technological Sciences, N.S.W., Australia

Received 12 May 1986; Revised 13 August 1986. Available online 3 May 2004.

* Research Assistant with the National Fund for Scientific Research, Belgium, whose support is acknowledged.

** Supported by NSF Grants No. 85-13400.

Abstract

The rate of parameter convergence in a number of adaptive estimation schemes is related to the smallest eigenvalue of the average information matrix determined by the regression vector. Using a very simple examples, we illustrate that the input signals that maximize this minimum eigenvalue may be quite different from the input signals that optimize more classical input design criteria, e.g. D-optimal criterion.

Author Keywords: Exponential convergence; Persistence of excitation; Experiment design