Global internal stabilizability does not imply global external stabilizability for small sensor disturbances

Author

Freeman, Randy

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

40

Issue

12

fYear

1995

fDate

12/1/1995 12:00:00 AM

Firstpage

2119

Lastpage

2122

Abstract

It was shown by Sontag (ibid., vol.34, no.4, p.435-43 (1989)) that for control-affine nonlinear systems, global asymptotic stabilizability via continuous state feedback implies global input-to-state stabilizability with respect to actuator disturbances. We show that the analogous result for sensor disturbances does not hold: we construct a second-order system which admits a continuous memoryless globally asymptotically stabilizing state feedback controller but for which no such controller can prevent finite escape times from every initial condition in the presence of small sensor disturbances

Keywords

asymptotic stability; memoryless systems; nonlinear control systems; sensors; state feedback; affine nonlinear systems; asymptotic stabilizability; continuous memoryless controller; continuous state feedback; global external stabilizability; global internal stabilizability; second-order system; sensor disturbances; Actuators; Asymptotic stability; Control systems; Control theory; Nonlinear control systems; Nonlinear systems; Robust stability; Sensor systems; State feedback; Working environment noise;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.478336

Filename

478336