A limit to the capability of feedback

Abstract

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 paper, we 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 (L) of the uncertain nonlinear function under consideration. It is shown that, if p and L satisfy the following relationship: L+ 1/2 /spl ges//sup (1+p)//spl radic/(pL)(1+1/p), where pL>1, then there exists no globally stabilizing feedback for the corresponding class of uncertain systems, and we thus find a quantitative limit to the capability of the feedback mechanism in dealing with structural uncertainties.