A Global Asymptotic Stability Result for a Class of Totally Asynchronous Discrete Nonlinear Systems

Abstract.

This paper proves a global stability result for a class of nonlinear discrete-time systems that are subject to regular desynchronization, also known as total asynchronism. The class of systems studied has its origins in a discrete-time neural net model. The techniques used are of interest in terms of the use of a Lyapunov function for the study of convergence of asynchronous nonlinear dynamical systems and also in terms of applications to neural networks. In the latter context, the main result of this paper strengthens a result of an earlier paper on neural networks, and shows that a class of discrete-time continuous-valued neural nets of the Hopfield type displays global convergence properties even when there exists total asynchronism in the updating of neuron states.