We present a new approach to verifying contraction and L2-gain of uncertain nonlinear systems, extending the well-known method of integral quadratic constraints. The uncertain system consists of a feedback interconnection of a nonlinear nominal system and uncertainties satisfying differential integral quadratic constraints. A pointwise linear matrix inequality condition is formulated to verify the closed-loop differential L2 gain, which can lead to global reference-independent L2 gain performance of the nonlinear uncertain system. For a polynomial nominal system, the convex verification conditions can be solved via sum-of-squares programming. A simple computational example based on jet-engine surge with input delays illustrates the approach.
@article{arxiv.1903.08806,
title = {Robust Contraction Analysis of Nonlinear Systems via Differential IQC},
author = {Ruigang Wang and Ian R. Manchester},
journal= {arXiv preprint arXiv:1903.08806},
year = {2019}
}