Generalized stability conditions for Takagi-Sugeno fuzzy time-delay systems
Generalized stability conditions for Takagi-Sugeno fuzzy time-delay systems
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DOI：
10.1109/iccis.2004.1460464
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发表时间：
2004-12
期刊：
影响因子：
--
通讯作者：
J. Yoneyama
中科院分区：
文献类型：
--
作者：
J. Yoneyama
本文研究了Takagi-Sugeno模糊时滞系统的广义时滞相关稳定性条件。在文献中，已经得到了模糊时滞系统的时滞无关稳定性条件和时滞相关稳定性条件。然而，这些条件相当保守，并不能保证广泛的稳定区域。对于模糊时滞系统的镇定控制器的设计也是如此，这也导致了模糊控制器的保守设计。首先对模糊时滞系统进行了广义变换，得到了广义时滞相关稳定性条件。在这样的广义变换中，我们有一些任意的矩阵来推广系统表示。事实上，这些矩阵不仅推广了系统的表示，而且推广了时滞相关的稳定性条件。时滞相关条件依赖于时滞的上界，并以线性矩阵不等式(LMI)的形式给出。然后，我们将我们的广义时滞相关稳定性条件与文献中的其他稳定性条件进行了比较，证明了我们的条件是广义时滞相关稳定性条件。接下来，我们考虑镇定问题。基于我们的广义时滞相关稳定性条件，我们得到了闭环系统稳定的时滞相关充分条件。最后，我们给出一个简单的例子来说明我们的结果。
In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy time-delay systems. In the literature, both delay-independent stability conditions and delay-dependent stability conditions for fuzzy time-delay systems have already been obtained. However, those conditions are rather conservative and do not guarantee wide stability regions. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first make a generalized transformation of fuzzy time-delay system to obtain generalized delay-dependent stability conditions. In such a generalized transformation, we have some arbitrary matrices that generalize a system representation. In fact, these matrices generalize not only the system representation but also delay-dependent stability conditions. Delay-dependent conditions depend on the upper bound of time-delay and are given in linear matrix inequalities (LMIs). Then, we compare our generalized delay-dependent stability condition with other stability conditions in the literature, and show that our condition is a generalized one. Next, we consider the stabilization problem. Based on our generalized delay-dependent stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be stable. Finally, we give a simple example that illustrates our result.