On the controllability of the continuous-time Hopfield-type neural networks

In this paper, the dependence of the steady states on the external input vector I for the analytical Hopfield-type neural network is discussed. It is shown that in some conditions, for any input vector I belonging to a certain set, the system has a unique steady state x = x(I) which depends analytically on I. Conditions for the local exponential stability of the steady state x(I) are given and estimates of its region of attraction are obtained employing Lyapunov functions. The estimates are compared with those reported in the literature. Conditions assuring the transfer of a steady state x(I*) into a steady state x(I**) by successive changes of the external input vector I are obtained, i.e. the steady states can be controlled.