ℒ2-Gain of Double Integrators with Saturation Nonlinearity

Gonçalves, Jorge M. (2001) ℒ2-Gain of Double Integrators with Saturation Nonlinearity. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:2001.011]

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Abstract

This paper uses quadratic surface Lyapunov functions to efficiently check if a double integrator in feedback with a saturation nonlinearity has ℒ2-gain less than γ > 0. We show that for many such systems, the ℒ2-gain is non-conservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of 1. These results allow the us of classical analysis tools like µ-analysis or IQCs to analyze systems with double integrators and saturations, including servo systems like some mechanical systems, satellites, hard-disks, CD players, etc.

EPrint Type:	Monograph (Technical Report)
Additional Information:	The author would like to thank Chung-Yao Kao for helpful comments and suggestions.
Subjects:	All Records
ID Code:	163
Deposited By:	Caltech Library System
Deposited On:	24 March 2008
Unique Identifier:	CaltechCDSTR:2001.011
Official Persistent URL:	http://resolver.caltech.edu/CaltechCDSTR:2001.011
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

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