Global Exponential Synchronization of Clifford-Valued Memristive Fuzzy Neural Networks with Delayed Impulses

The global exponential synchronization of Clifford-valued memristive fuzzy neural networks (CLVMFNNs) with delayed impulses and time-varying delays is investigated. The Clifford-valued NNs are an extension of complex-valued and quaternion-valued NNs. In order to describe the system as realistically as possible, Clifford-valued memristive fuzzy neural networks with delayed impulses and time-varying delays are established. To avoid non-commutativity of the multiplication of Clifford numbers, Clifford-valued neural networks are decomposed into real-valued neural networks. To explore the exponential stability of delayed impulsive systems, a novel lemma is proposed by using Halanay differential inequality. To induce the global exponential synchronization, a novel and simple linear feedback controller is designed. Sufficient conditions are given to ensure the global exponential synchronization using the proposed novel lemma under the designed feedback controller. Compared with the previous results, the conditions given in this paper are more effective and less conservative. A numerical simulation is given to verify the effectiveness of the theoretical results.