Relaxed Exponential Stabilization for Coupled Memristive Neural Networks With Connection Fault and Multiple Delays via Optimized Elastic Event-Triggered Mechanism.

This article investigates the problem of relaxed exponential stabilization for coupled memristive neural networks (CMNNs) with connection fault and multiple delays via an optimized elastic event-triggered mechanism (OEEM). The connection fault of the two or some nodes can result in the connection fault of other nodes and cause iterative faults in the CMNNs. Therefore, the method of backup resources is considered to improve the fault-tolerant capability and survivability of the CMNNs. In order to improve the robustness of the event-triggered mechanism and enhance the ability of the event-triggered mechanism to process noise signals, the time-varying bounded noise threshold matrices, time-varying decreased exponential threshold functions, and adaptive functions are simultaneously introduced to design the OEEM. In addition, the appropriate Lyapunov-Krasovskii functionals (LKFs) with some improved delay-product-type terms are constructed, and the relaxed exponential stabilization and globally uniformly ultimately bounded (GUUB) conditions are derived for the CMNNs with connection fault and multiple delays by means of some inequality processing techniques. Finally, two numerical examples are provided to illustrate the effectiveness of the results.

Multiple Mismatched Synchronization for Coupled Memristive Neural Networks With Topology-Based Probability Impulsive Mechanism on Time Scales.

This article is concerned with the exponential synchronization of coupled memristive neural networks (CMNNs) with multiple mismatched parameters and topology-based probability impulsive mechanism (TPIM) on time scales. To begin with, a novel model is designed by taking into account three types of mismatched parameters, including: 1) mismatched dimensions; 2) mismatched connection weights; and 3) mismatched time-varying delays. Then, the method of auxiliary-state variables is adopted to deal with the novel model, which implies that the presented novel model can not only use any isolated system (regard as a node) in the coupled system to synchronize the states of CMNNs but also can use an external node, that is, not affiliated to the coupled system to synchronize the states of CMNNs. Moreover, the TPIM is first proposed to efficiently schedule information transmission over the network, possibly subject to a series of nonideal factors. The novel control protocol is more robust against these nonideal factors than the traditional impulsive control mechanism. By means of the Lyapunov-Krasovskii functional, robust analysis approach, and some inequality processing techniques, exponential synchronization conditions unifying the continuous-time and discrete-time systems are derived on the framework of time scales. Finally, a numerical example is provided to illustrate the effectiveness of the main results.

Extended Robust Exponential Stability of Fuzzy Switched Memristive Inertial Neural Networks With Time-Varying Delays on Mode-Dependent Destabilizing Impulsive Control Protocol.

This article investigates the problem of robust exponential stability of fuzzy switched memristive inertial neural networks (FSMINNs) with time-varying delays on mode-dependent destabilizing impulsive control protocol. The memristive model presented here is treated as a switched system rather than employing the theory of differential inclusion and set-value map. To optimize the robust exponentially stable process and reduce the cost of time, hybrid mode-dependent destabilizing impulsive and adaptive feedback controllers are simultaneously applied to stabilize FSMINNs. In the new model, the multiple impulsive effects exist between two switched modes, and the multiple switched effects may also occur between two impulsive instants. Based on switched analysis techniques, the Takagi-Sugeno (T-S) fuzzy method, and the average dwell time, extended robust exponential stability conditions are derived. Finally, simulation is provided to illustrate the effectiveness of the results.

Exponential synchronization of stochastic delayed memristive neural networks via a novel hybrid control.

This paper investigates the exponential synchronization issue of stochastic delayed memristive neural networks (SDMNNs) via a novel hybrid control (HC), where impulsive instants are determined by the state-dependent trigger condition. The switching and quantification strategies are applied to the event-based impulsive controller to cope with the challenges induced concurrently by interval parameters, impulses, stochastic disturbance and time-varying delays. Furthermore, the control costs can be reduced and communication channels and bandwidths can be saved by using this designed controller. Then, novel Lyapunov functions and new analytical methods are constructed, which can be used to realize the exponential synchronization of SDMNNs via HC. Finally, a numerical simulation is provided to demonstrate our theoretical results.