Stochastic quantized control for memristive neural networks with mixed semi-Markov jump and sampled-data communications using a novel approach

In this paper, the issue of stability and stabilization for semi-Markov jump memristive neural networks (SMJMNNs) with stochastic quantized sampled-data control (QSDC) law is addressed. Firstly, a memristive neural network (MNN) model with mixed semi-Markov jump is established in the framework of the three independent Markov chains. Then, a stochastic QSDC scheme is proposed, in which semi-Markov jump parameters (SMJPs) in the gain matrices, quantization parameters and system connection weight matrices are different from each other. On the other hand, since signal transmission may be delayed, the influence of transmission delay is considered in the proposed stochastic QSDC scheme. Based on the above, a more general weak infinitesimal operator about the three semi-Markov processes (SMPs) is first given to deal with stochastic Lyapunov functionals (LFs). To reduce the conservatism of the obtained results, stochastic LFs about the two-sided closed-loop functions are constructed in the framework of the sampling patterns 6(tk) to 6(t) and 6(t) to 6(tk+1). Then, based on the novel constructed LFs, stochastic stability criterion for SMJMNNs is established by combining with stochastic QSDC law. Finally, the numerical simulation examples are provided to verify the validity and less conservatism of the obtained theoretical results.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, the authors address the issue of stability and stabilization for semi-Markov jump memristive neural networks (SMJMNNs) with stochastic quantized sampled-data control (QSDC) law. They establish a model of memristive neural network (MNN) with mixed semi-Markov jump and propose a stochastic QSDC scheme that considers the influence of transmission delay. They also develop a more general weak infinitesimal operator and construct stochastic Lyapunov functionals (LFs) to reduce conservatism and establish a stochastic stability criterion for SMJMNNs based on the constructed LFs.