Exponential synchronization control of delayed memristive neural network based on canonical Bessel-Legendre inequality

<abstract><p>In this paper, we study the exponential synchronization problem of a class of delayed memristive neural networks(MNNs). Firstly, a intermittent control scheme is designed to solve the parameter mismatch problem of MNNs. A discontinuous controller with two tunable scalars is designed, and the upper limit of control gain can be adjusted flexibly. Secondly, an augmented Lyaponov-Krasovskii functional(LKF) is proposed, and vector information of N-order canonical Bessel-Legendre(B-L) inequalities is introduced. LKF method is used to obtain the stability criterion to ensure exponential synchronization of the system. The conservatism of the result decreases with the increase of the order of the B-L inequality. Finally, the effectiveness of the main results is verified by two simulation examples.</p></abstract>

Stabilization of Periodical Discrete Feedback Control for Markov Jumping Stochastic Systems

Motivated by the two strategies of intermittent control and discrete feedback control, this paper aims to introduce a periodically intermittent discrete feedback control in the drift part to stabilize an unstable Markov jumping stochastic differential system. It is illustrated that, by the approach of comparison principle, this can be achieved in the sense of almost sure exponential stability. Further, the stabilization theory is applied to Markov jumping stochastic recurrent neural networks.

Fixed-Time Synchronization of Neural Networks Based on Quantized Intermittent Control for Image Protection

This paper considers the fixed-time synchronization (FIXTS) of neural networks (NNs) by using quantized intermittent control (QIC). Based on QIC, a fixed-time controller is designed to ensure that the NNs achieve synchronization in finite time. With this controller, the settling time can be estimated regardless of initial conditions. After ensuring that the system has stabilized through this strategy, it is suitable for image protection given the behavior of the system. Meanwhile, the encryption effect of the image depends on the encryption algorithm, and the quality of the decrypted image depends on the synchronization error of NNs. The numerical results show that the designed controller is effective and validate the practical application of FIXTS of NNs in image protection.