@inproceedings{11ef231a44d04430bde1d3712beba108,
title = "Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networks",
abstract = "This paper presents sufficient conditions for the stability and ℓ2-gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are derived by combining Lyapunov/dissipativity theory with Quadratic Constraints (QCs) satisfied by repeated ReLUs. We write a general class of QCs for repeated ReLUs using known properties for the scalar ReLU. Our stability and performance condition uses these QCs along with a 'lifted' representation for the ReLU RNN. We show that the positive homogeneity property satisfied by a scalar ReLU does not expand the class of QCs for the repeated ReLU. We present examples to demonstrate the stability / performance condition and study the effect of the lifting horizon.",
author = "Noori, {Sahel Vahedi} and Bin Hu and Geir Dullerud and Peter Seiler",
note = "The authors acknowledge AFOSR Grant #FA9550-23-1- 0732 for funding of this work.; 63rd IEEE Conference on Decision and Control, CDC 2024 ; Conference date: 16-12-2024 Through 19-12-2024",
year = "2024",
doi = "10.1109/CDC56724.2024.10886894",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "8626--8632",
booktitle = "2024 IEEE 63rd Conference on Decision and Control, CDC 2024",
address = "United States",
}