Non-smooth stabilizers for nonlinear systems with uncontrollable unstable linearization

Author

Qian, Chunjiang ; Lin, Wei

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Case Western Reserve Univ., Cleveland, OH, USA

Volume

2

fYear

2000

fDate

2000

Firstpage

1655

Abstract

We prove that every chain of odd power integrators perturbed by a C¹ triangular vector field can be stabilized in the large via continuous state feedback, although it is not stabilizable, even locally, by any smooth state feedback. The proof is constructive and accomplished by developing a machinery-a continuous type of adding a power integrator-that enables one to explicitly design a C⁰ globally stabilizing feedback law as well as a C¹ control Lyapunov function which is positive definite and proper

Keywords

Lyapunov methods; asymptotic stability; control system synthesis; nonlinear control systems; state feedback; C⁰ globally stabilizing feedback law; C¹ control Lyapunov function; C¹ triangular vector field; continuous state feedback; nonsmooth stabilizers; odd power integrators; uncontrollable unstable linearization; Asymptotic stability; Books; Chromium; Control systems; Eigenvalues and eigenfunctions; Jacobian matrices; Linear feedback control systems; Nonlinear systems; Robust stability; State feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on

Conference_Location

Sydney, NSW

ISSN

0191-2216

Print_ISBN

0-7803-6638-7

Type

conf

DOI

10.1109/CDC.2000.912099

Filename

912099