State estimation of TakagiSugeno systems with unmeasurable premise variables
State estimation of TakagiSugeno systems with unmeasurable premise variables
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DOI：
10.1049/iet-cta.2009.0054
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发表时间：
2010
影响因子：
2.6
通讯作者：
D. Ichalal;B. Marx;J. Ragot;D. Maquin
中科院分区：
文献类型：
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作者：
D. Ichalal;B. Marx;J. Ragot;D. Maquin
本文研究了具有不可测前提变量的Takagi-Sugeno（T-S）多模型非线性系统的观测器设计问题。此外，与具有可测前提变量的T-S系统相比，这种T-S结构可以表示更大类的非线性系统。将系统的状态作为前提变量，可以精确地表示由一般形式stecx/f（x，u）描述的非线性系统。然而，已有的基于实测前提变量的T-S系统状态估计方法并不直接适用于以状态作为前提变量的系统。本文首先给出了具有不可测前提变量的T-S系统的观测器设计，并通过李雅普诺夫稳定性分析给出了观测器的充分收敛条件。利用线性矩阵不等式（LMI）的形式，以表达的状态估计误差的收敛条件，并获得观测器的增益。其次，所提出的方法进行了扩展，以衰减能量有界的未知输入，如干扰。最后通过一个算例对现有的一些方法和本文提出的方法进行了比较。
: This study is dedicated to the design of observers for non-linear systems described by Takagi–Sugeno (T–S) multiple models with unmeasurable premise variables. Furthermore, this T–S structure can represent a larger class of non-linear systems compared to the T– S systems with measurable premise variables. Considering the state of the system as a premise variable allows one to exactly represent the non-linear systems described by the general form ˙ x ¼ f ( x, u ). Unfortunately, the developed methods for estimating the state of T–S systems with measured premise variable are not directly applicable for the systems that use the state as a premise variable. In the present paper, firstly, the design of observers for T– S systems with unmeasurable premise variable is proposed and sufficient convergence conditions are established by Lyapunov stability analysis. The linear matrix inequality (LMI) formalism is used in order to express the convergence conditions of the state estimation error in terms of LMI and to obtain the gains of the observer. Secondly, the proposed method is extended in order to attenuate energy-bounded unknown inputs such as disturbances. An academic example is proposed to compare some existing methods and the proposed one.