Stabilization of nonlinear systems with uncontrollable linearization

Author

Behtash, S. ; Sastry, S.

Author_Institution

Dept. of Electr. Eng., California Univ., Berkeley, CA, USA

Volume

33

Issue

6

fYear

1988

fDate

6/1/1988 12:00:00 AM

Firstpage

585

Lastpage

590

Abstract

The problem of local stabilization of nonlinear control systems with linearizations that contain uncontrollable modes on the imaginary axis is considered. A methodology of designing a stabilizing control is investigated. It involves the following steps: (1) reduction of the stability problem to the stability of the center manifold system, (2) simplification of the vector field on the center manifold using the theory of normal forms, and (3) finding conditions under which the simplified vector field is asymptotically stable. Three cases of degeneracies in the linearized system are treated, and sufficient conditions for the existence of stabilizing controls are given in each case. A theorem is presented regarding the robustness of the above control strategies

Keywords

nonlinear control systems; stability; center manifold system; nonlinear control systems; robustness; stability; stabilizing control; uncontrollable linearization; Asymptotic stability; Control systems; Design methodology; Eigenvalues and eigenfunctions; Jacobian matrices; Nonlinear control systems; Nonlinear systems; Robust control; State feedback; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.1259

Filename

1259