Title: On a frame theoretic measure of quality of LTI systems,
Abstract: It is of practical significance to define the notion of a measure of quality
of a control system, i.e., a quantitative extension of the classical notion of
controllability. In this article we demonstrate that the three standard
measures of quality involving the trace, minimum eigenvalue, and the
determinant of the controllability grammian achieve their optimum values when
the columns of the controllability matrix from a tight frame. Motivated by
this, and in view of some recent developments in frame theoretic signal
processing, we provide a measure of quality for LTI systems based on a measure
of tightness of the columns of the reachability matrix .