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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. doi:10.1109/TAC.2002.805674.

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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.

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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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9772
Deposited By: Archive Administrator
Deposited On:14 Mar 2008
Last Modified:08 Nov 2021 21:02

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