Quantized Control Based on Stabilization of Discontinuous Memristor-Based Fuzzy Inertial Neural Networks With Proportional Delays

In this article, the finite-time (FnT) control of a class of discontinuous memristor-based fuzzy inertial neural networks with proportional delays is discussed. The proposed model is more generalized. Different from the use of the finite/fixed-time stability lemmas in the previous works, by constructing the unit ball and discussing the subordinate relationship between the states and the unit ball, the finite/fixed-time stability are analyzed in detail. This method can avoid the rough thinking that the state variables of the system start from greater than 1. Also, the control constraint is taken into account and a quantized controller is designed, which can not only help achieve the finite/fixed-time stability, but also can prevent the singularity when using the norm forms and chattering when using the sign function in the controllers. In addition, the energy consumptions generated by the quantized controller are estimated in FnT and fixed-time stability processes. The criteria show that the energy consumptions are relevant to the proportional delays, when the proportional coefficient is 1, the energy loss reaches the minimum value. Finally, numerical example and simulation are provided to verify the validity of the obtained results.