Observers for Lipschitz nonlinear systems

Author

Rajamani, Rajesh

Author_Institution

California Univ., Berkeley, CA, USA

Volume

43

Issue

3

fYear

1998

fDate

3/1/1998 12:00:00 AM

Firstpage

397

Lastpage

401

Abstract

This paper presents some fundamental insights into observer design for the class of Lipschitz nonlinear systems. The stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix. The correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented. These conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix. The eigenvalues have to be located sufficiently far out into the left half-plane, and the eigenvectors also have to be sufficiently well-conditioned for ensuring asymptotic stability. Based on these results, a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

Keywords

asymptotic stability; control nonlinearities; control system synthesis; eigenvalues and eigenfunctions; nonlinear systems; observers; Lipschitz nonlinear systems; asymptotic stability; eigenvalues; gain matrix; necessary conditions; nonlinearity; observer; stability matrix; sufficient conditions; Algorithm design and analysis; Asymptotic stability; Eigenvalues and eigenfunctions; Estimation error; Linearity; Nonlinear systems; Riccati equations; Robots; Sufficient conditions; Yield estimation;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.661604

Filename

661604