Minimal root sensitivity in linear systems

Abstract

Nominal performance, root sensitivity, and stability are important control design considerations. This paper deals only with the first two of these concerns. A lower bound is derived for root sensitivity and necessary and sufficient conditions are given to achieve this minimum. This is the main result of the paper. In addition, an optimal output feedback control problem is discussed which penalizes an index related to root sensitivity. Two hazards are clarified concerning root sensitivity designs. First, we illustrate that root sensitivity has nothing to do with stability. Second, we show that normality of the plant matrix is the necessary and sufficient condition for minimal root sensitivity, but that normality measures can be convex even when root sensitivity measures are not. Hence, the optimization problems are quite different, and normality objectives cannot always be substituted for root sensitivity objectives.

A Unifying Framework for Finite Wordlength Realizations

“…It is easy to see that (26) and so (25) leads to the following transfer function sensitivity measure:…”

“…Mantey [25] showed that the poles/eigenvalues are dependent on the state-space realization. It is wellknown that an eigenvalue sensitivity is minimized if the system is normal [26]. However Gevers and Li [5] subsequently determined the realization that would minimize a pole sensitivity measure combined with a zero sensitivity measure proposed in [27].…”