Predefined- Time Robust Synchronization for Competitive Neural Networks with Fast-Slow Time Scales: Sliding-Mode Control Approach

In this paper, the predefined-time (PdT) synchro-nization for competitive neural networks (CNNs) exhibiting multiple time scales with parametric and external disturbances is investigated on the basis of the sliding-mode control. The new PdT stability theorems for the singular perturbation system are derived and the appropriate autonomous controllers and suitable integral sliding-mode surfaces are designed. Consequently, the PdT drive-response synchronization for the CNNs is established, independent of other additional algebraic conditions. The error states of drive-response CNNs can reach and keep on the designed surfaces within a PdT, causing the states to approach zero. Moreover, the PdT, as an arbitrary positive constant, is treated as a controller parameter, offering good flexibility in advance. Finally, the numerical example is provided to illustrate the effectiveness of the obtained main results.