Stability of memristor neural networks with delays operating in the flux-charge domain

The paper considers a class of neural networks where flux-controlled dynamic memristors are used in the neurons and finite concentrated delays are accounted for in the interconnections. Goal of the paper is to thoroughly analyze the nonlinear dynamics both in the flux-charge domain and in the current-voltage domain. In particular, a condition that is expressed in the form of a linear matrix inequality, and involves the interconnection matrix, the delayed interconnection matrix, and the memristor nonlinearity, is given ensuring that in the flux-charge domain the networks possess a unique globally exponentially stable equilibrium point. The same condition is shown to ensure exponential convergence of each trajectory toward an equilibrium point in the voltage-current domain. Moreover, when a steady state is reached, all voltages, currents and power in the networks vanish, while the memristors act as nonvolatile memories keeping the result of computation, i.e., the asymptotic values of fluxes. Differences with existing results on stability of other classes of delayed memristor neural networks, and potential advantages over traditional neural networks operating in the typical voltage-current domain, are discussed.