The Eigenstructure of Linear High Gain Feedback Systems

The regulation and transmission properties of linear time invariant continuous high gain feedback systems are considered. These properties are derived directly from the eigenstructure of the system closed loop dynamic matrix which depends, for high gain feedback, on the zero structure of the open loop system. Use is being made of the dependency to find explicit expressions for the dominant components of the asymptotic eigenstructure in terms of the system matrices and these expressions are applied in the analysis of the state trajectories and the derivation of the transmission properties of the high gain feedback servo-system. The conditions for perfect regulation are readily found. The transmission properties of the corresponding system are then shown to be equivalent to those of a lower order system that is independent of the open loop dynamic matrix.