IEEE Trans Syst Man Cybern B Cybern. 2012 Aug;42(4):1053-63. doi: 10.1109/TSMCB.2012.2185842. Epub 2012 Feb 29.
This paper is concerned with the problem of state estimation for a class of discrete-time chaotic systems with or without time delays. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these systems, such as chaotic neural networks, Chua's circuits, Hénon map, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, H∞ state estimator are designed for this model with sensors to guarantee the asymptotic stability of the estimation error dynamic systems and to reduce the influence of noise on the estimation error. The parameters of these filters are obtained by solving the eigenvalue problem. As most discrete-time chaotic systems with or without time delays can be described with this unified model, H∞ state estimator design for these systems can be done in a unified way. Three numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.
本文关注一类具有或不具有时间延迟的离散时间混沌系统的状态估计问题。采用由线性动态系统和有界静态非线性算子组成的统一模型来描述这些系统，如混沌神经网络、蔡氏电路、亨农映射等。基于使用线性矩阵不等式方法对该统一模型进行的H∞性能分析，为该模型设计了带传感器的H∞状态估计器，以保证估计误差动态系统的渐近稳定性，并减少噪声对估计误差的影响。这些滤波器的参数通过求解特征值问题获得。由于大多数具有或不具有时间延迟的离散时间混沌系统都可以用这个统一模型来描述，因此可以以统一的方式对这些系统进行H∞状态估计器设计。利用三个数值例子来说明所提出的估计器设计方案的有效性。
