Necessary and sufficient conditions for robust stability of a class of nonlinear systems

Author

Gonçalves, Jorge M. ; Dahleh, Munther A.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA

Volume

1

fYear

1995

fDate

13-15 Dec 1995

Firstpage

401

Abstract

Input-output stability results for feedback systems are developed. Robust stability conditions are presented for nonlinear systems with nonlinear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small gain theorem for a class of these systems is presented. Then it is also shown that, for the vector spaces (l_∞, ||·||_∞) and (l₂, ||·||₂), the sufficient conditions are also necessary with some additional assumptions on the systems. These results capture the conservatism of the small gain theorem as it is applied to systems that do not need to have linear gain

Keywords

feedback; input-output stability; nonlinear control systems; robust control; uncertain systems; feedback systems; input-output stability; necessary and sufficient conditions; nonlinear systems; nonlinear uncertainty; robust stability; sufficient small gain theorem; vector spaces; Feedback loop; Gain; Laboratories; Nonlinear systems; Robust stability; Robustness; Sufficient conditions; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.478823

Filename

478823