Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model

Conference paper (2018)

Authors

Dušan Stipanović University of Illinois at Urbana Champaign
Boris Murmann Stanford University
Matteo Causo Université Grenoble Alpes
A. Lekić University of Belgrade
Vicenç Rubies-Royo University of California
Claire Tomlin University of California
Edith Beigne Université Grenoble Alpes
Sebastien Thuries Université Grenoble Alpes
Mykhailo Zarudniev Université Grenoble Alpes
Suzanne Lesecq Université Grenoble Alpes
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Published Date

26-04-2018

Language

English

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Abstract

In this paper some local stability results for an autonomous Long Short-Term Memory neural network model with respect to the origin are provided. In particular, it is shown through linearization that the local asymptotic stability conditions with respect to the origin only depend on one of the weight matrices. Simulations indicate that these local stability conditions greatly influence the behavior of the autonomous four-dimensional neural network in the region where each variable's values vary between minus one and one. Finally, some sufficient stability conditions for the nonlinear model are formulated as a convex program involving linear matrix inequalities.