Liu Xiaoyang, Cao Jinde
Department of Mathematics, Southeast University, Nanjing 210096, China.
IEEE Trans Syst Man Cybern B Cybern. 2010 Dec;40(6):1425-37. doi: 10.1109/TSMCB.2009.2039478. Epub 2010 Feb 17.
Discontinuous dynamical systems, particularly neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. In this paper, the robust state estimation problem is investigated for uncertain neural networks with discontinuous activations and time-varying delays, where the neuron-dependent nonlinear disturbance on the network outputs are only assumed to satisfy the local Lipschitz condition. Based on the theory of differential inclusions and nonsmooth analysis, several criteria are presented to guarantee the existence of the desired robust state estimator for the discontinuous neural networks. It is shown that the design of the state estimator for such networks can be achieved by solving some linear matrix inequalities, which are dependent on the size of the time derivative of the time-varying delays. Finally, numerical examples are given to illustrate the theoretical results.
非连续动力系统，特别是具有非连续激活函数的神经网络，出现在许多应用中，并且近年来受到了相当多的研究关注。本文研究了具有非连续激活和时变延迟的不确定神经网络的鲁棒状态估计问题，其中仅假设网络输出上依赖于神经元的非线性干扰满足局部Lipschitz条件。基于微分包含理论和非光滑分析，提出了几个准则来保证非连续神经网络所需鲁棒状态估计器的存在性。结果表明，此类网络的状态估计器设计可通过求解一些依赖于时变延迟时间导数大小的线性矩阵不等式来实现。最后，给出了数值例子来说明理论结果。
