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ℒ2-Gain of Double Integrators with Saturation Nonlinearity

Gonçalves, Jorge M. (2001) ℒ2-Gain of Double Integrators with Saturation Nonlinearity. California Institute of Technology , Pasadena, CA. (Unpublished)

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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.

Item Type:Report or Paper (Technical Report)
Additional Information:The author would like to thank Chung-Yao Kao for helpful comments and suggestions.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:2001.011
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28134
Deposited By: Imported from CaltechCDSTR
Deposited On:24 Mar 2008
Last Modified:03 Oct 2019 03:29

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