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ℒ2-Gain of double integrators with saturation nonlinearity

Gonçalves, Jorge M. (2002) ℒ2-Gain of double integrators with saturation nonlinearity. IEEE Transactions on Automatic Control, 47 (12). pp. 2063-2068. ISSN 0018-9286. https://resolver.caltech.edu/CaltechAUTHORS:GONieeetac02

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Abstract

This note uses quadratic surface Lyapunov functions (SuLFs) 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 nonconservative 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 use of classical analysis tools like µ-analysis or integral quadratic constraints to analyze systems with double integrators and saturations, including servo systems like some mechanical systems, satellites, hard disks, compact disk players, etc.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TAC.2002.805674DOIUNSPECIFIED
Additional Information:© Copyright 2002 IEEE. Reprinted with permission. Manuscript received December 19, 2001; revised June 25, 2002 and August 13, 2002. Recommended by Associate Editor Z. Lin.
Subject Keywords:Double integrator, impact map, nonlinear robust analysis, quadratic surface Lyapunov function, saturation
Issue or Number:12
Record Number:CaltechAUTHORS:GONieeetac02
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:GONieeetac02
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9772
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:14 Mar 2008
Last Modified:03 Oct 2019 00:03

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