ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems
ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems
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DOI：
10.1002/rnc.1169
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发表时间：
2007-08
影响因子：
3.9
通讯作者：
Ligang Wu;Zidong Wang;Huijun Gao;Changhong Wang
中科院分区：
文献类型：
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作者：
Ligang Wu;Zidong Wang;Huijun Gao;Changhong Wang
本文研究了二维（2-D）离散时间线性变参数（LPV）系统的l2-l ∞和l2-l∞滤波问题。基于著名的Fornasini-Marchesini局部状态空间（FMLSS）模型，通过引入参数变化现象，建立了所考虑的2-D系统的数学模型。所解决的问题的目的是设计全阶滤波器，使得滤波误差动态是渐近稳定的，并且可以分别实现在l2-l∞和l2-l∞意义下的规定的噪声衰减水平。参数化线性矩阵不等式（PLMIs），推导出存在这样的过滤器的充分条件，相应的过滤器的综合问题，然后转化为一个凸优化问题，可以有效地解决使用标准的软件包。仿真实例验证了该方法的有效性和实用性。版权所有© 2007约翰威利父子有限公司。
In this paper, the ℋ︁∞ and l2–l∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ℋ︁∞ and l2–l∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ℋ︁∞ and l2–l∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method. Copyright © 2007 John Wiley & Sons, Ltd.