Controllability and stability radii for companion form systems

This paper describes a unifying approach to the computation of certain robustness measures for some calculations involving state space models in control and system theory. These measures include nearness to uncontrollability, nearness to instability, and nearness to unstabilizability and their duals. Specialized results are provided for systems in companion form (controllability canonical form, etc.). It is shown analytically why high-order companion system models have certain undesirable numerical properties. For example, it is shown that almost all highorder companion matrices are nearly singular and almost all high-order controllable canonical forms are nearly uncontrollable. This research was supported by the Office of Naval Research under Contract No. N00014-85-K-0553 and the National Science Foundation (and AFOSR) under Grant No. ECS-8718897.