L_2-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 £_2-gain less than y > 0. We show that for many of such systems, the £_2-gain is non-conservative in the sense that they are approximately equal to the lower bound obtained by lacing the saturation with a constant gain of 1. These results allow the use of classical analysis tools like p-analysis or IQCs to analyze systems with double integrators and saturations, including seru, systems like some mechanical systems, satellites, hard-disks, CD players, etc.

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