Sliding mode control-based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays

In this article, we are interested in the fixed-time stabilization (FTSt) and fixed-time synchronization (FTSy) of a class of inertial neural networks with time-varying and distributed delays. To obtain FTSt and FTSy, sliding mode controllers are developed based on sliding mode control techniques and by using sliding variables. Two polynomial feedback control laws are exploited to achieve the FTSt and the FTSy but they are singular. To get rid of the singularities, the saturation function is used into the design of the controllers and the almost FTSt and almost FTSy are proved. Finally, numerical examples are presented to show the effectiveness of the theoretical results.