ℓ1-gain Filter Design of Discrete-time Positive Neural Networks with Mixed Delays
ℓ1-gain Filter Design of Discrete-time Positive Neural Networks with Mixed Delays
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DOI：
10.1016/j.neunet.2019.10.004
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Shunyuan Xiao;Yijun Zhang;Baoyong Zhang
中科院分区：
文献类型：
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作者：
Shunyuan Xiao;Yijun Zhang;Baoyong Zhang
本文主要研究了一类离散时间正神经网络具有1增益干扰抑制性能的滤波器设计。考虑了神经元传递过程中出现的离散和分布时变延迟。特别地，在系统模型中，用伯努利随机过程描述了分布式延迟的概率分布。首先，给出了离散时间神经网络的正均衡性和唯一均衡性准则。其次，通过线性Lyapunov方法，给出了正神经网络具有全局渐近稳定且增益为1的扰动抑制性能的充分条件。第三，利用上述结果，给出了所建立的滤波误差系统的增益稳定性判据，并在此基础上提出了线性规划（LP）方法来设计期望的正滤波器。最后，以配水网络和遗传调控网络为例，验证了所得结果的有效性和适用性。
This paper mainly focuses on the filter design with ℓ 1-gain disturbance attenuation performance for a class of discrete-time positive neural networks. Discrete and distributed time-varying delays occurring in neuron transmission are taken into account. Especially, the probabilistic distribution of distributed delays is described by a Bernoulli random process in the system model. First, criteria on the positiveness and the unique equilibrium of discrete-time neural networks are presented. Second, through linear Lyapunov method, sufficient conditions for globally asymptotic stability with ℓ 1-gain disturbance attenuation performance of positive neural networks are proposed. Third, using the results obtained above, criteria on ℓ 1-gain stability of the established filtering error system are presented, based on which a linear programming (LP) approach is put forward to design the desired positive filter. Finally, two examples of applications to water distribution network and genetic regulatory network are given to demonstrate the effectiveness and applicability of the derived results.