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arXiv · 1903.08806

Robust Contraction Analysis of Nonlinear Systems via Differential IQC

Ruigang Wang·Ian R. Manchester
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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.

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Ruigang Wang, Ian R. Manchester. 2019-03-21. Robust Contraction Analysis of Nonlinear Systems via Differential IQC. https://arxiv.org/abs/1903.08806

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