A limit to the capability of feedback

Author

Zhang, Yanxia ; Guo, Lei

Author_Institution

Inst. of Syst. Sci., Acad. Sinica, Beijing, China

Volume

2

fYear

2001

fDate

2001

Firstpage

2013

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.981206

Filename

981206