New Predefined-Time Stability Theorem and Applications to the Fuzzy Stochastic Memristive Neural Networks with Impulsive Effects

The paper mainly investigates the issue of achieving predefined-time synchronization for fuzzy memristive neural networks with both impulsive effects and stochastic disturbances. Firstly, due to the fact that the existed predefined-time stability theorems can hardly be applied to systems with impulsive effects, a new predefined-time stability theorem is proposed to solve the stability problem of the systems with impulsive effects. The theorem is flexible and can guide impulsive stochastic fuzzy memristive neural network models to achieve predefined-time synchronization. Secondly, due to the limitation problems for sign function that it can easily lead to cause the chattering phenomenon, resulting in undesirable results such as decreased synchronization performance. A novel and effective feedback controller without the sign function is designed to eliminate this chattering phenomenon in the paper. In addition, The paper overcomes the comprehensive influence of fuzzy logic, memristive state dependence and stochastic disturbance, and gives the effective conditions to ensure that two stochastic systems can achieve the predefined-time synchronization. Finally, the effectiveness of the proposed theoretical results is demonstrated in detail through a numerical simulation.