Improved results on finite-time synchronization of shunting inhibitory cellular neural networks with time-varying delays via impulsive pinning hybrid control

This paper explores finite-time synchronization in shunting inhibitory cellular neural networks (SICNNs) with time-varying delays. A novel hybrid controller is introduced, which operates as an adaptive-feedback controller during impulsive intervals and switches to a pinning controller with impulsive-feedback action at impulsive instants, similar to the doublet pinning mode. Considering the basic Lyapunov function, we have proposed the settling-times for finite-time synchronization characteristics of the SICNNs-based master-slave model structured along with the hybrid controller and subdomains. The effectiveness of the proposed approach is validated through case studies, and the settling-times are comparatively analyzed using the Lambert $W$ function. This theoretical analysis demonstrates the advantages of the proposed hybrid controller over impulsive adaptive hybrid and traditional adaptive-feedback controllers. A numerical example highlights the effectiveness of the proposed hybrid controller, with MATLAB simulations aligning closely with manual computations. Finally, the comparison includes assessing the proposed hybrid controller over impulsive adaptive hybrid and conventional adaptive-feedback controllers.