On complete stability of linear and quadratic programming neural networks

The paper addresses complete stability (CS) of the important class of neural networks to solve linear and quadratic programming problems introduced by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35:554). By CS it is meant that each trajectory converges to a stationary state, i.e. an equilibrium point of the neural network. It is shown that the neural networks in (IEEE Trans. Circuits Syst., 1988; 35:554) enjoy the property of CS even in the most general case where there are infinite non-isolated equilibrium points. This result, which is proved by exploiting a new method to analyse CS (Int. J Bifurcation Chaos 2001; 11:655), extends the stability analysis by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35:554) to situations of interest where the optimization problems have infinite solutions. Copyright (C) 2002 John Wiley Sons, Ltd.