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We present a new approach to verifying contraction and $L_2$-gain ofuncertain nonlinear systems, extending the well-known method of integralquadratic constraints. The uncertain system consists of a feedbackinterconnection of a nonlinear nominal system and uncertainties satisfyingdifferential integral quadratic constraints. A pointwise linear matrixinequality condition is formulated to verify the closed-loop differential $ L_2$ gain, which can lead to global reference-independent $ L_2 $ gain performanceof the nonlinear uncertain system. For a polynomial nominal system, the convexverification conditions can be solved via sum-of-squares programming. A simplecomputational example based on jet-engine surge with input delays illustratesthe approach.

Robust Contraction Analysis of Nonlinear Systems via Differential IQC