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Published December 14, 2001 | public
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ℒ2-Gain of Double Integrators with Saturation Nonlinearity

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.

Additional Information

The author would like to thank Chung-Yao Kao for helpful comments and suggestions.

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Additional details

Created:
August 19, 2023
Modified:
October 24, 2023