This paper tackles the problem of piecewise affine memory filtering design for the discrete-time norm-bounded uncertain Takagi_Sugeno fuzzy affine systems. The objective is to design an admissible filter using past output measurements of the system, guaranteeing the asymptotic stability of the filtering error system with a given H∞{\mathscr H}_{\infty } performance index. Based on the piecewise fuzzy Lyapunov functions and the projection lemma, a new sufficient condition for H∞\mathscr H_{\infty } filtering performance analysis is first derived, and then the filter synthesis is carried out. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities. In addition, it is also shown that the filtering performance can be improved with the increasing number of past output measurements used in the filtering design. Finally, two examples are presented to show the advantages and effectiveness of the proposed approach.

中文翻译：

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使用过去的输出测量的 T__ 模糊仿射系统的新型分段仿射滤波设计


本文解决了离散时间范数有界不确定 Takagi_Sugeno 模糊仿射系统的分段仿射记忆滤波设计问题。目标是使用系统过去的输出测量来设计可接受的滤波器，保证具有给定的 H∞{\mathscr H}_{\infty } 性能指标的滤波误差系统的渐近稳定性。基于分段模糊Lyapunov函数和投影引理，首先推导了H∞\mathscr H_{\infty }滤波性能分析的新充分条件，然后进行滤波器综合。结果表明，滤波器增益可以通过求解一组线性矩阵不等式来获得。此外，还表明，随着滤波设计中使用的过去输出测量次数的增加，可以提高滤波性能。最后，通过两个例子来展示该方法的优点和有效性。