Stability of Discrete time Recurrent Neural Networks and Nonlinear optimization problems

TL;DR

This paper introduces a new method based on reducing the dissipativity domain to establish global Lyapunov stability in discrete-time recurrent neural networks, surpassing traditional criteria in effectiveness.

Contribution

It develops a multi-step procedure involving nonconvex function maximization over polytopes, providing stronger stability conditions for nonlinear neural systems.

Findings

The method proves more powerful than standard stability criteria.

Conditions for unique local maxima over hyperplanes are derived.

Applicable to a wide range of neuron transfer functions.

Abstract

We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems produce rather weak results. The method mentioned above is proved to be more powerful. It involves a multi-step procedure with maximization of special nonconvex functions over polytopes on every step. We derive conditions which guarantee an existence of at most one point of local maximum for such functions over every hyperplane. This nontrivial result is valid for wide range of neuron transfer functions.