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

In this paper we analyses the problem of continuity of the closed-loop system map as a function of the compensator parameters. Under a suitable parameterization 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)≥n where the plant is a p x 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> O.