Nonlinear High Gain Separation Principles and Fast Sampling Results ensuring Robust Stability

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Description/Abstract

A semi-global nonlinear separation principle is described which presents conditions under which a stabilizing controller based on the output and its derivatives (typically the state or partial state) can be replaced by a controller based on measurement of the output only. The results include the case of high gain observer reconstruction of the output derivatives and the case of approximating the output derivatives via numerical derivatives for which various realizable schemes based on discrete sampling are given. The same sampling constructions and results are also applied directly to the output measurement itself, giving rise to fast sampling theorems. The proofs are based on estimating gap distances between the original controller and the reconstructed approximation and conditions based on the robust stability margin.