Synchronization and control of discrete incommensurate fractional-order and variable-order neural networks

The examination of dynamics and synchronization within discrete fractional neural networks has attracted notable interest in contemporary studies. Nevertheless, current research has primarily focused on commensurate discrete fractional-order neural networks. This study aims to explore the synchronization of incommensurate discrete fractional neural networks, spanning both constant and variable orders. By employing linear feedback control techniques, we establish a satisfactory criterion to guarantee the synchronization of noncommensurate discrete fractional neural networks with constant orders. This condition is formulated in terms of linear matrix inequalities, offering a systematic approach to synchronization. Furthermore, under specific conditions, the Lyapunov functional is employed to analyze the synchronization of noncommensurate discrete fractional neural networks with variable orders. This synchronization condition is solely dependent on the system parameters, facilitating easy verification and implementation. In order to confirm the efficacy and practicality of the proposed methodologies, two numerical examples are selected and presented, demonstrating the successful synchronization of incommensurate discrete fractional neural networks.