Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model
Dušan M. Stipanović, Boris Murmann, Matteo Causo, Aleksandra Lekić, Vicenç Rúbies Royo, Claire Jennifer Tomlin, Édith Beigné, Sébastien Thuries, Mykhailo Zarudniev, Suzanne Lesecq · 2018
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.