Long-Short Term Memory Neural Network Stability and Stabilization using Linear Matrix Inequalities

Shankar A. Deka, Dusan M. Stipanovic, Boris Murmann, Claire J. Tomlin

Abstract: A global asymptotic stability condition for Long Short-Term Memory neural networks is presented in this paper. A linear matrix inequality optimization problem is used to describe this global stability condition. The linear matrix inequality formulation can be viewed as a way for stabilization of Long Short-Term Memory neural networks since the networks' weight matrices and biases can be essentially treated as control variables. The condition and how to compute numerical values for the weight matrices and biases are illustrated by some examples.