A limit to the capability of feedback

Feedback is ubiquitous and is a basic concept in the area of control, where it is used primarily for reducing internal or external uncertainties, or both. In this note, we will study the capability of feedback in dealing with both internal and external uncertainties for a class of pth order nonlinear autoregressive control systems. The size of the uncertainty is described by the Lipschitz constant (say L) of the uncertain nonlinear function in consideration. It is shown that if p and L satisfy a certain inequality, then there exists no globally stabilizing feedback for the corresponding class of uncertain systems, and thus finding a quantitative limit to the capability of the feedback mechanism in dealing with structural uncertainties.