Finite/Fixed-Time Synchronization of Memristor-Based Fuzzy Neural Networks with Markov Jumping Parameters Under Unified Control Schemes

This paper proposes a unified framework to achieve the finite/fixed-time synchronization of memristor-based fuzzy delayed neural networks considering both Markov jumping phenomenon and external disturbance. Under the designed common controller, by regulating its main control parameters, the goals of finite-time and fixed-time synchronization for the network can be achieved separately. Besides, by integrating algebraic inequality technologies, the fuzzy set theory and Lyapunov theory, a new finite/fixed-time theorem can be obtained for the drive-response system. Taking into account more complex Lyapunov–Krasovskii functional involving mode-dependent terms and double integral terms, is more closer to practical applications than those in the existing results. Finally, an example is presented to substantiate the effectiveness of the theoretical results.