Title :
A limit to the capability of feedback
Author :
Zhang, Yanxia ; Guo, Lei
Author_Institution :
Inst. of Syst. Sci., Acad. Sinica, Beijing, China
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+½⩾(1+p)√(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
Keywords :
autoregressive processes; feedback; nonlinear control systems; nonlinear functions; stability; uncertain systems; Lipschitz constant; control; external uncertainty reduction; feedback capability limit; globally stabilizing feedback; internal uncertainty reduction; pth-order nonlinear autoregressive control systems; structural uncertainties; uncertain nonlinear function; uncertain systems; Adaptive control; Automatic control; Control systems; Control theory; Feedback loop; Programmable control; Robust control; Stability; Uncertain systems; Uncertainty;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.981206
