Exponential Convergence Estimates for a Single Neuron System of Neutral-Type

The future behavior of a dynamical system is determined by its initial state or initial function. Nontrivial neuron system involving adaptive learning corresponds to the memorization of initial information. In this paper, exponential estimates and sufficient conditions for the exponential stability of a single neuron system of neutral-type are studied. Of particular importance is the fact that exponential convergence guarantees that this system is capable of memorizing initial functions. Furthermore, this system is also capable of conveying much more information with respect to the initial functions memorized by neuron system with time delay. The proofs follow some new results on nonhomogeneous difference equations evolving in continuous-time combined with the Lyapunov-Krasovskii functional and the descriptor system approach. The exponential stability conditions are expressed in terms of a linear matrix inequality, which lead to less restrictive and less conservative exponential estimates.