A New Geometric Stability Margin for Feedback Systema.

Abstract

This paper provides a new geometric concept for a stability margin for feedback control systems which is applicable for any number of inputs and outputs. The measure of stability margin employed has the advantage over standard mesaures of exposing certain additional internal stability properties of a feedback configuration employing dynamic compensation. The stability margin is based on the essential topological features of an Abstract Nyquist criterion proposed by Brockett and Byrnes. This abstract Nyquist criterion for multivariable systems involves the topology of intersectiona between certain pairs of subspaces of the direct sum of the system inputs and outputs. The measures employed here are derived from the idea of principal angles between a pair of subspaces. Some examples are given which highlight the differences between these mesaures and other more standard measures.