The peaking phenomenon and the global stabilization of nonlinear systems

Author

Sussmann, H.J. ; Kokotovic, P.V.

Author_Institution

Dept. of Math., Rutgers Univ., New Brunswick, NJ, USA

Volume

36

Issue

4

fYear

1991

fDate

4/1/1991 12:00:00 AM

Firstpage

424

Lastpage

440

Abstract

The problem of global stabilization is considered for a class of cascade systems. The first part of the cascade is a linear controllable system and the second part is a nonlinear system receiving the inputs from the states of the first part. With zero input, the equilibrium of the nonlinear part is globally asymptotically stable. In linear systems, a peaking phenomenon occurs when high-gain feedback is used to produce eigenvalues with very negative real parts. It is established that the destabilizing effects of peaking can be reduced if the nonlinearities have sufficiently slow growth. A detailed analysis of the peaking phenomenon is provided. The tradeoffs between linear peaking and nonlinear growth conditions are examined

Keywords

control nonlinearities; control system analysis; eigenvalues and eigenfunctions; feedback; nonlinear systems; stability; cascade systems; eigenvalues; feedback; global stabilization; linear controllable system; nonlinear systems; nonlinearities; peaking phenomenon; stability; Content addressable storage; Control systems; Eigenvalues and eigenfunctions; H infinity control; Hydrogen; Iron; Linear systems; Negative feedback; Nonlinear systems; State feedback;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.75101

Filename

75101