Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays
Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays
复制标题
DOI：
10.1016/j.ins.2007.11.022
复制
发表时间：
2008-04
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
本文研究了具有离散时滞和分布时滞的Takagi-Sugeno模糊系统的时滞相关稳定性条件。虽然离散时滞模糊系统的稳定性条件已经有很多种，但分布时滞模糊系统的稳定性条件几乎没有文献报道。对于具有分布时滞的不确定模糊系统的鲁棒稳定性问题也是如此。在这里，我们采用广义李雅普诺夫泛函得到的离散和分布时滞的模糊系统的时滞相关稳定性条件。我们引入一些自由的加权矩阵，这样的李雅普诺夫功能，以减少保守性的稳定性条件。这些技术导致广义和保守性较低的稳定性条件。我们还考虑了具有不确定参数的模糊时滞系统的鲁棒稳定性。应用同样的技术，稳定性条件，我们得到了时滞相关的充分条件的不确定模糊系统的离散和分布时滞的鲁棒稳定性。此外，我们考虑了状态反馈镇定。基于稳定性和鲁棒稳定性条件，得到了状态反馈控制器镇定模糊时滞系统的条件。最后，我们给出了两个例子来说明我们的结果。这里得到的时滞相关的稳定性条件，以保证一个广泛的稳定区域。
In this paper, we consider delay-dependent stability conditions of Takagi–Sugeno fuzzy systems with discrete and distributed delays. Although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained, almost no stability condition for fuzzy systems with distributed delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed delays. Here we employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of fuzzy systems with discrete and distributed delays. We introduce some free weighting matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative stability conditions. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we give two examples to illustrate our results. Delay-dependent stability conditions obtained here are shown to guarantee a wide stability region.