Robust Contraction Analysis of Nonlinear Systems via Differential IQC

Abstract

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.

submitted to CDC2019

References in corpus (2)

• Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming
• Contraction analysis of switched Filippov systems via regularization