Synchronization and state estimation for discrete-time complex networks with distributed delays
Synchronization and state estimation for discrete-time complex networks with distributed delays
复制标题
具有分布式延迟的离散时间复杂网络的同步和状态估计
DOI：
10.1109/tsmcb.2008.925745
复制
发表时间：
2008-10-01
影响因子：
--
通讯作者：
Liu, Xiaohui
中科院分区：
文献类型：
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作者：
Liu, Yurong;Wang, Zidong;Liu, Xiaohui
本文研究了一类同时存在离散时滞和分布时滞的耦合复杂离散网络的同步问题。复杂的网络，包括神经网络和社会网络作为特殊情况是相当普遍的。与通常使用的lipschitz型函数不同，本文采用了一种更一般的类扇区非线性函数来描述网络中存在的非线性。首先定义了离散域上的分布无限时滞。利用一种新颖的Lyapunov-Krasovskii泛函和Kronecker积，证明了当某些线性矩阵不等式（lmi）可行时，具有分布式延迟的寻址离散时间复杂网络是同步的。然后研究了同一复杂网络的状态估计问题，其目的是设计一个状态估计器，通过可用的输出测量来估计网络状态，使得对于所有允许的离散和分布延迟，估计误差的动态保证全局渐近稳定。对于状态估计问题，又提出了一种LMI方法。通过两个仿真实例验证了所提出的全局同步和状态估计条件的有效性。值得指出的是，即使网络中的标称子系统不稳定，我们的主要结果也是有效的。
In this paper, a synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays. The complex networks addressed which include neural and social networks as special cases are quite general. Rather than the commonly used Lipschitz-type function, a more general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. The distributed infinite time delays in the discrete-time domain are first defined. By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed discrete-time complex network with distributed delays is synchronized if certain linear matrix inequalities (LMIs) are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, for all admissible discrete and distributed delays, the dynamics of the estimation error is guaranteed to be globally asymptotically stable. Again, an LMI approach is developed for the state estimation problem. Two simulation examples are provided to show the usefulness of the proposed global synchronization and state estimation conditions. It is worth pointing out that our main results are valid even if the nominal subsystems within the network are unstable.