Controller Design for Synchronization of Neural Networks with Time-varying Delays and Hybrid Couplings

Abstract

Recently, the network synchronization has been challenging and interesting in var- ious applications such as signal processing, communication, and so on. In this thesis, the synchronization problems for coupled neural networks with time-varying delays and hybrid couplings are investigated. The goal of this research is to study and introduce a general array model of coupled delayed neural networks with hybrid couplings for handling synchronization problem. Global and exponential synchronization of coupled neural net- works are studied and analyzed. For global synchronization, the coupled neural networks with simultaneous presence the discrete and unbounded distributed delays are studied in the case of constant and interval time-varying delay couplings. For exponential syn- chronization, the coupled neural networks with presence leakage delay is studied in the case of constant, interval time-varying delay and distributed delay couplings. Further- more, the problem of synchronization designed by controller is studied as well. In this research, the global synchronization for hybrid coupled neural networks are proposed by feedback and sampled-data feedback controls. The exponential synchronization for hy- brid coupled neural networks with feedback and intermittent feedback controls are further studied. Based on the design of inner-coupling, outer-coupling, and some free matrices representing the relationships between the system matrices, some sufficient conditions are systematically established to meet the synchronization by constructing the improved Lyapunov-Krasovskii functionals and Kronecker product properties. Numerical examples with their simulations and the obtained results are given to show the effectiveness of the proposed method