Analysis of Lurie Systems With Magnitude Nonlinearities and Connections to Neural Network Stability Analysis

• 成果类型: Article
• 署名作者: Richardson, Carl R.; Turner, Matthew C.; Gunn, Steve R.
• 署名单位: University of Oxford; University of Southampton
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3665137
• 发表日期: 2026

摘要

This article considers the interconnection of a continuous time linear time-invariant system and a multivariable magnitude nonlinearity. A number of different quadratic constraints are established for the magnitude nonlinearity and then used to derive stability criteria based on quadratic and Lurie-type Lyapunov functions. The new stability criteria are cast as matrix inequalities and in some cases solved using semidefinite programming. Connections are made between the magnitude nonlinearity and neural network activation functions, such as the rectified linear unit (ReLU) and leaky ReLU, effectively allowing the stability criteria derived here to be used to analyze interconnections of dynamical systems and neural networks. Using the positive homogeneity property, shared by the (leaky) ReLU and magnitude functions, mild conditions are also established to show that the existence of a unique equilibrium point is sufficient for local and global stability to be equivalent. Finally, the new global stability criteria are tested on several numerical examples, including a Hopfield network with 100 states and neurons, and compared favorably with competing criteria from the literature.