Richardson, C.R., Turner, M.C., Gunn, S.R. et al. (1 more author) (2024) Strengthened stability analysis of discrete-time Lurie systems involving ReLU neural networks. In: Proceedings of Machine Learning Research. 6th Annual Learning for Dynamics & Control Conference, 15-17 Jul 2024, Oxford, United Kingdom. ML Research Press , pp. 209-221.
Abstract
This paper addresses the stability analysis of a discrete-time (DT) Lurie system featuring a static repeated ReLU nonlinearity. Such systems often arise in the analysis of recurrent neural networks and other neural feedback loops. Custom quadratic constraints, satisfied by the repeated ReLU, are employed to strengthen the standard DT Circle and DT Popov Criteria for this specific Lurie system. The criteria can be expressed as a set of linear matrix inequalities (LMIs) with less restrictive conditions on the matrix variables. It is further shown that if the Lurie system under consideration has a unique equilibrium point at the origin, then this equilibrium point is in fact globally stable or unstable, meaning that local stability analysis will provide no additional benefit. Numerical examples demonstrate that the strengthened criteria achieve a desirable balance between reduced conservatism and complexity when compared to existing criteria.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 C. R. Richardson, M. C. Turner, S. R. Gunn & R. Drummond. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > School of Electrical and Electronic Engineering |
Funding Information: | Funder Grant number ROYAL ACADEMY OF ENGINEERING (THE) ICRF\113 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Jan 2025 15:12 |
Last Modified: | 17 Jan 2025 15:13 |
Published Version: | https://proceedings.mlr.press/v242/richardson24a.h... |
Status: | Published |
Publisher: | ML Research Press |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221800 |