New Generalized Stability Conditions for Takagi-Sugeno Fuzzy Time-Delay Systems
New Generalized Stability Conditions for Takagi-Sugeno Fuzzy Time-Delay Systems
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DOI：
10.1109/fuzzy.2005.1452523
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发表时间：
2005-05
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
在本文中，我们考虑 Takagi-Sugeno 模糊时滞系统的新广义时滞相关稳定性条件。文献中已经获得了模糊时滞系统的时滞无关稳定条件和时滞相关稳定条件。然而，这些条件相当保守，并不能保证广泛的稳定区域。在为模糊时滞系统设计稳定控制器的情况下也是如此，因此也导致了保守的模糊控制器设计。这里我们在原始模糊时滞系统中引入一个辅助系统来获得广义时滞相关的稳定性条件。在辅助系统中，我们有一些任意矩阵来概括系统表示。事实上，这个辅助系统不仅概括了系统表示，还概括了延迟相关的稳定性条件。我们在这里获得的延迟相关条件取决于时间延迟的上限，并以线性矩阵不等式（LMI）给出。然后，我们将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比较，并表明我们的条件是广义的。接下来，我们考虑稳定性问题。基于广义的时滞相关稳定性条件，我们获得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 new 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 also true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. Here we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. In the auxiliary system, we have some arbitrary matrices that generalize a system representation. In fact, this auxiliary system generalizes not only the system representation but also delay-dependent stability conditions. Delay-dependent conditions we obtain here depend on the upper bound of time-delay and are given in linear matrix inequalities (LMI's). 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