ℒ2 gain bounds for systems with slope-restricted nonlinearities

This paper proposes a new method for calculating a bound on the ℒ₂ gain of a system consisting of a linear time invariant (LTI) part and a static nonlinear part, which is odd, bounded, zero at the origin and has a restriction on its slope. The problem is posed in the IQC framework and the ℒ₂ gain bound is found by solving a set of linear matrix inequalities (LMIs). The novelty of the paper lies in the use of a recent characterisation of the multiplier for systems with slope-restricted nonlinearities. Examples illustrate the effectiveness of the results against the state-of-the-art.