A weak L2-gain property for nonlinear systems

Author

Dower, Peter M. ; Kellett, Christopher M. ; Huan Zhang

Author_Institution

Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia

fYear

2012

fDate

10-13 Dec. 2012

Firstpage

2286

Lastpage

2291

Abstract

Nonlinear L₂-gain is a generalization of the conventional (linear) notion of L₂-gain in which the linear scaling of input energy is replaced by a nonlinear comparison function scaling. In this paper, this nonlinear L₂-gain property is formalized as being strictly weaker than the conventional linear property. This is achieved by appealing to existing results in the literature that demonstrate qualitative equivalences between linear L₂-gain and input-to-state stability (ISS), and between nonlinear L₂-gain and the strictly weaker integral ISS (iISS) property.

Keywords

input-output stability; nonlinear control systems; nonlinear dynamical systems; iISS property; input energy linear scaling; input-to-state stability; linear L₂-gain property; nonlinear function scaling; qualitative equivalences; strictly weaker integral ISS property; strictly weaker nonlinear weak L₂-gain property; Gain; Inspection; Nonlinear systems; Robust stability; Stability criteria; Transient analysis; L2-gain analysis; input-to-state stability; integral input-to-state stability; nonlinear systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2012 IEEE 51st Annual Conference on

Conference_Location

Maui, HI

ISSN

0743-1546

Print_ISBN

978-1-4673-2065-8

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2012.6425918

Filename

6425918