Synchronizing Neural Networks With Proportional Delays Based on a Class of $q$-Type Allowable Time Scales

Without confines of the continuous-time domain, this paper addresses synchronization control problem of neural networks in the face of multiple proportional delays on general time scales. The idea to deal with proportional delays is to propose a class of
$q$
-type allowable time scales on which we design an appropriate controller to achieve exponential synchronization based on a calculus theory on time scales and Lyapunov function/functional methods. It is shown that adopting properties of
$q$
-type time scales is an effective approach to establish synchronization for the networks with proportional delays. This helps us to have insight into the synchronization problems on general intermittent time domain. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.