Stability Analysis And Synchronization Control Design Of Delayed Memristive Neural Networks

Neurons, neuronal and non neuronal cells in the brain are interconnected through the synapse and then the information can be transferred, while memristor is proved to have the nonlinear electrical properties similar to the plastic response of brain synapses under bioelectrical signals, thus memristor can be used to mimic synapse, which results in the construction of circuit of memristor-based neural network. By replacing the resistor in cir-cuit of traditional recurrent neural network with memristor so as to simulate the synapse, this paper designs several classes of dynamic systems for delayed memristive neural net-works and studies the stability and synchronization control problem. These theories lay a theoretical foundation of the memory elements in applications such as the nerve bionics, the dynamic memories of informations and the chaotic secure communications.Delayed memristive neural networks are a class of state-dependent switched system-s, so the classical stability theory for the differential equations with continuous right-hand sides cannot be applied here. Under the framework of discontinuous stability theory of Filip-pov and by using the theories of differential inclusions and set-value maps, this dissertation analyzes the dynamic behaviors of delayed memristive neural networks, including the pas-sivity, finite-time stabilizability and instabilizability, adaptive synchronizationand General decay synchronization. The main research contents of this paper are presented as follows.The passivity of a class of delayed memristive neural networks is discussed. Different from previous publications, the time-varying delays of the systems are not necessary to be differentiable. Under the general condition of delays, new passivity conditions based on linear matrix inequality are established for delayed memristive neural networks. Theoretical and simulation results show that our results are more general and applicable compared with earlier results.The finite-time stabilizability and instabilizability problems for a class of delayed mem-ristive neural networks are analyzed via a nonlinear controller. The designed nonlinear con-troller is general, and by choosing different parameters of the same controller, different cri- teria concerning the finite-time stabilizability and the instabilizability of delayed memristive neural networks are obtained in terms of M-matrix. Due to the operation and efficiency of practical engineering practice, finite-time stability control (stabilization) is of great practical significance.The synchronization of a class of delayed memristive neural networks is studied under adaptive feedback control. A new error is defined by properly introducing a function ?(t). The choice of ?(t) is flexible, so synchronization including not only traditional exponential and asymptotical synchronization but also logarithmical and polynomial synchronization are obtained. Compared with linear control, adaptive control method here is more flexible since the control gains of adaptive control increase according to the adaptive laws Compared with the linear control, the adaptive control method not only accords with the actual economic benefits and avoids waste, but also can be used to solve the synchronization control problem of other delayed systems.The synchronization with general decay rate for a class of delayed memristive neural networks is investigated under nonlinear feedback control. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ?-type synchronization (synchronization with general decay rate) are established via the designed nonlinear feedback control. The ?-type synchronization is in a general framework and it cannot be realized by the linear control. Actually, it contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases.