Recent papers in the literature introduced a class of neural networks (NNs) with memristors, named dynamic-memristor (DM) NNs, such that the analog processing takes place in the charge-flux domain, instead of the typical current-voltage domain as it happens for Hopfield NNs and standard cellular NNs. One key advantage is that, when a steady state is reached, all currents, voltages, and power of a DM-NN drop off, whereas the memristors act as nonvolatile memories that store the processing result. Previous work in the literature addressed multistability of DM-NNs, i.e., convergence of solutions in the presence of multiple asymptotically stable equilibrium points (EPs). The goal of this paper is to study a basically different dynamical property of DM-NNs, namely, to thoroughly investigate the fundamental issue of global asymptotic stability (GAS) of the unique EP of a DM-NN in the general case of nonsymmetric neuron interconnections. A basic result on GAS of DM-NNs is established using Lyapunov method and the concept of Lyapunov diagonally stable matrices. On this basis, some relevant classes of nonsymmetric DM-NNs enjoying the property of GAS are highlighted.

DI MARCO, M., Forti, M., Pancioni, L. (2018). New conditions for global asymptotic stability of memristor neural networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 29(5), 1822-1834 [10.1109/TNNLS.2017.2688404].

New conditions for global asymptotic stability of memristor neural networks

DI MARCO, MAURO;FORTI, MAURO;PANCIONI, LUCA
2018-01-01

Abstract

Recent papers in the literature introduced a class of neural networks (NNs) with memristors, named dynamic-memristor (DM) NNs, such that the analog processing takes place in the charge-flux domain, instead of the typical current-voltage domain as it happens for Hopfield NNs and standard cellular NNs. One key advantage is that, when a steady state is reached, all currents, voltages, and power of a DM-NN drop off, whereas the memristors act as nonvolatile memories that store the processing result. Previous work in the literature addressed multistability of DM-NNs, i.e., convergence of solutions in the presence of multiple asymptotically stable equilibrium points (EPs). The goal of this paper is to study a basically different dynamical property of DM-NNs, namely, to thoroughly investigate the fundamental issue of global asymptotic stability (GAS) of the unique EP of a DM-NN in the general case of nonsymmetric neuron interconnections. A basic result on GAS of DM-NNs is established using Lyapunov method and the concept of Lyapunov diagonally stable matrices. On this basis, some relevant classes of nonsymmetric DM-NNs enjoying the property of GAS are highlighted.
2018
DI MARCO, M., Forti, M., Pancioni, L. (2018). New conditions for global asymptotic stability of memristor neural networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 29(5), 1822-1834 [10.1109/TNNLS.2017.2688404].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1013270