Robust H∞ Filtering for 2D Stochastic Systems
Robust H∞ Filtering for 2D Stochastic Systems
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DOI：
10.1007/s00034-004-1121-0
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发表时间：
2004-12
期刊：
影响因子：
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通讯作者：
Huijun Gao;J. Lam;Changhong Wang;Shengyuan Xu
中科院分区：
文献类型：
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作者：
Huijun Gao;J. Lam;Changhong Wang;Shengyuan Xu
研究了二维(2D)随机系统的H-∞滤波器设计问题。首次将随机扰动引入著名的Fornasini-Marchesini局域状态空间模型。我们的注意力集中在全阶和降阶滤波器的设计上，它们保证滤波误差系统是均方渐近稳定的，并具有给定的H∞干扰抑制性能。以线性矩阵不等式的形式给出了这类滤波器存在的充分条件，并将相应的滤波器设计问题转化为一个凸优化问题，利用现有的数值软件可以有效地处理该问题。此外，将所得结果进一步推广到更一般的情况，即系统矩阵也含有不确定参数的情况。最常用的处理参数不确定性的方法，包括多面体特征和范数有界特征，都被考虑在内。最后给出了一个数值算例来说明所提出的滤波器设计方法的有效性。
This paper investigates the problem of H∞filter design for two-dimensional (2D) stochastic systems. The stochastic perturbation is first introduced into the well-known Fornasini-Marchesini local state-space model. Our attention is focused on the design of full-order and reduced-order filters, which guarantee the filtering error system to be mean-square asymptotically stable and to have a prescribed H∞disturbance attenuation performance. Sufficient conditions for the existence of such filters are established in terms of linear matrix inequalities, and the corresponding filter design is cast into a convex optimization problem, which can be efficiently handled by using available numerical software. In addition, the obtained results are further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, are taken into consideration. A numerical example is provided to illustrate the usefulness of the proposed filter design procedures.