Liang Jinling, Wang Zidong, Liu Xiaohui
Department of Mathematics, Southeast University, Nanjing 210096, China.
IEEE Trans Neural Netw. 2009 May;20(5):781-93. doi: 10.1109/TNN.2009.2013240. Epub 2009 Mar 27.
This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.
本文研究一类具有测量缺失和时变延迟的离散时间耦合不确定随机复杂网络的状态估计问题。假设参数不确定性是范数有界的，并且同时存在于网络状态和网络输出中。随机布朗运动不仅影响网络的耦合项，还影响整个网络动态。状态方程和测量方程中均存在满足通常利普希茨条件的非线性项。通过由服从条件概率分布的二元切换序列描述的可用输出测量，我们旨在设计一个状态估计器来估计网络状态，使得对于所有允许的参数不确定性和时变延迟，估计误差动态在均方意义下保证全局指数稳定。通过采用李雅普诺夫泛函方法结合随机分析方法，建立了几个依赖于延迟的准则，以确保所需估计器增益的存在，然后根据某些线性矩阵不等式（LMI）的解来表征此类估计器增益的显式表达式。利用两个数值例子来说明所提出的估计器设计方案的有效性。
