Exponential $\mathcal {H}_{\infty }$ Filtering for Discrete-Time Switched Neural Networks With Random Delays
Exponential $\mathcal {H}_{\infty }$ Filtering for Discrete-Time Switched Neural Networks With Random Delays
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DOI：
10.1109/tcyb.2014.2332356
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发表时间：
2015-04
影响因子：
11.8
通讯作者：
K. Mathiyalagan;H. Su;P. Shi;R. Sakthivel
中科院分区：
文献类型：
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作者：
K. Mathiyalagan;H. Su;P. Shi;R. Sakthivel
研究了一类具有随机时变时滞的离散切换神经网络的指数H∞滤波问题。所涉及的延迟被假定为随机时变的，其特征在于通过引入一个伯努利随机变量。同时考虑了时滞的变化范围和分布概率的影响。假设非线性激活函数满足扇形条件。我们的目标是通过设计一个全阶滤波器来估计状态，使得滤波器误差系统是全局指数稳定的，具有期望的衰减率和H∞性能衰减水平。该滤波器采用分段Lyapunov-Krasovskii泛函、线性矩阵不等式（LMI）方法和平均驻留时间方法设计。首先建立了一组充分的LMI条件，保证增广系统的指数均方稳定性，然后将全阶滤波器的参数表示为一组LMI条件的解。建议的LMI条件可以很容易地解决，通过使用标准的软件包。最后，通过实际问题的数值例子来说明所提出的滤波器设计的有效性。
This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.