How exciting can a signal really be?

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.     

Fake algebraic Riccati techniques and stability

Conditions, sufficient and necessary, for monotonic behavior of the solutions of the Riccati differential equation and Riccati difference equation are derived. For the optimal filtering (respectively, control) equation these results are derived without the usual requirement of detectability (respectively, stabilizability). The monotonic behavior allows proof of stabilizing properties of the solutions, subject only to requirements on the initial conditions     

A miscellany of results of an equation of Count J. F. Riccati

A collection of results on the Riccati equation is presented. The questions addressed are the existence of strong solutions of the algebraic Riccati equation and the convergence of solutions of the Riccati difference equation to those of the algebraic equation. The results derived utilize detestability conditions only.