On a frame theoretic measure of quality of LTI systems
Provides a theoretical unification of existing controllability quality measures for control systems, but is incremental as it reframes known results in frame theory.
The paper shows that three standard quality measures of LTI systems (trace, minimum eigenvalue, determinant of controllability grammian) are optimized when the controllability matrix columns form a tight frame, and proposes a new quality measure based on frame tightness.
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 .