Robust Contraction Analysis of Nonlinear Systems via Differential IQC
For control theorists and engineers, this provides a new method to analyze robust stability and performance of uncertain nonlinear systems, though the example is simple and the computational scalability is not addressed.
The paper extends integral quadratic constraints to verify contraction and L2-gain for uncertain nonlinear systems, formulating a pointwise linear matrix inequality condition that enables global reference-independent performance. The approach is demonstrated on a jet-engine surge example with input delays.
We present a new approach to verifying contraction and $L_2$-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 $ L_2 $ gain, which can lead to global reference-independent $ L_2 $ 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.