High-gain feedback in non-linear control systems†

Abstract High-gain state and output feedback are investigated for non-linear control systems with a single additive input by using singular perturbation techniques. Classical approximation results (Tihonov-like theorems) in singular perturbation theory are extended to non-linear control systems by defining a composite additive control strategy, a control-dependent fast equilibrium manifold and non-linear change of coordinates. Those tools and an appropriate change of coordinates show that high-gain state feedback and variable structure control systems can be equivalently used for approximate non-linearity compensation in feedback-linearizable systems. Next the effect of high-gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility. For strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input-output feedback-linearizable transformation is applied. Notes †This work was partly supported by M.P.I, (fondi 40%).