Hybrid projective synchronization of complex-valued memristive neural networks via concise prescribed-time control strategies

This article aims to consider the prescribed-time hybrid projective synchronization of fully complex-valued memristive delayed neural networks with discontinuous activation. Above all, a new prescribed-time stability lemma is established, of which the settling time is directly a parameter of the auxiliary function and the conservatism of the conditions is reduced. Unlike common research methods, to simplify the operation, the complex-valued memristive neural network model is converted into one with uncertain parameters in view of the convex analysis approach. Subsequently, applying Filippov’s solution theory, prescribed-time stability theory, inequality techniques, and non-separation method, several novel and concise sufficient criteria are established to ensure the considered systems achieve prescribed-time synchronization by designing some controllers. Additionally, unlike common power-law type prescribed-time controllers, the ones designed in this paper are simpler because they do not involve sign function and time-delay term and have relatively fewer terms. Especially, one of their control gains is a time variable rather than a constant. And the prescribed synchronization time is independent of any initial values and parameters of the system, and can be preset arbitrarily according to actual needs. Compared with existing works, the hybrid projective coefficients of this paper are complex-valued that can be adjusted rather than real-valued, and projective synchronization, complete synchronization and anti-synchronization are its special cases. Eventually, numerical simulation results are furnished to manifest the effectiveness of the acquired theoretical outcomes.