Conference Proceedings

A weak L-2-gain property for nonlinear systems

Peter M Dower, Christopher M Kellett, Huan Zhang

2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC) | IEEE | Published : 2012

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. © 2012 IEEE.

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Awarded by ARC Discovery


Funding Acknowledgements

P.M. Dower and H. Zhang are with the Department of Electrical & Electronic Engineering, University of Melbourne, Melbourne, Victoria, Australia {pdower,hzhang5}@unimelb.edu.au. Dower and Zhang are supported by AFOSR grant FA2386-09-1-4111 and ARC Discovery Project DP120101549 C.M. Kellett is with the School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, New South Wales, Australia Chris.Kellett@newcastle.edu.au. Kellett is supported by ARC Future Fellowship 110100746.