Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks’ weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.