Convergence analysis of linear dynamical systems by high gain and high dynamic compensation

Abstract

In this paper we analyse the problem of continuity of the closed-loop system map as a function of the compensator parameters. Under a suitable parametrization of the compensators we show that a necessary and sufficient condition for the closed-loop systems map to be continuous is given by max (>m, p) ≤ where the plant is a >p × >m plant of degree n. In particular, for single-input single-output plants, the closed-loop systems map is always continuous. The above result is surprising because the inequality is independent of the McMillan degree >q of the compensator. We also analyse the pole placement map and show that it always has points of discontinuity whenever >q > 0.