The Exponential Stability and Asynchronous Stabilization of a Class of Switched Nonlinear System Via the T–S Fuzzy Model
The Exponential Stability and Asynchronous Stabilization of a Class of Switched Nonlinear System Via the T–S Fuzzy Model
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DOI：
10.1109/tfuzz.2013.2276762
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发表时间：
2014-08
影响因子：
11.9
通讯作者：
Y. Mao;Hongbin Zhang;Shengyuan Xu
中科院分区：
文献类型：
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作者：
Y. Mao;Hongbin Zhang;Shengyuan Xu
本文研究了一类非线性切换系统的指数稳定性和异步镇定问题。采用T-S模糊模型来逼近次非线性动态系统。利用两层函数，即清晰切换函数和局部模糊权函数，我们引入了连续时间切换模糊系统，它内在地包含了切换混杂系统和T-S模糊系统的特征。利用构造的分段类Lyapunov函数和最小停留时间方法，得到了切换模糊系统的指数稳定性，使得系统中存在稳定和不稳定的非线性子系统。在实际应用中，对于控制问题，不可避免地要花费一定的时间来识别系统模式和应用匹配的控制器，系统模式切换和控制器切换之间普遍存在异步现象。基于稳定性结果，提出了切换模糊系统异步切换下的模糊状态反馈控制器。此外，最小停留时间的下界可以得到使用凸优化，使得切换模糊系统可以指数稳定，如果其最小停留时间是大于界。切换模糊系统的稳定性结果和控制律的线性矩阵不等式的形式，是数值上可行的。最后，给出了两个数值例子来说明所得到的理论结果的有效性。
In this paper, we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems. The Takagi and Sugeno (T-S) fuzzy model is employed to approximate the subnonlinear dynamic systems. With two-level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. By the use of delicately constructed piecewise Lyapunov-like functions (PLFs) and minimum dwell time method, we obtain the exponential stability of the switched fuzzy systems, which allows us to have stable and unstable nonlinear subsystems. In practice, for the control problem, it inevitably takes some time to identify the system modes and apply the matched controller, the asynchronous phenomena between the system modes switching and the controllers switching generally exists. Based on the result of stability, the fuzzy state feedback controller under asynchronous switching is proposed for switched fuzzy systems. In addition, the lower bound of minimum dwell time can be obtained using convex optimization such that the switched fuzzy system can be exponentially stabilized if its minimum dwell time is larger than the bound. The stability results and control laws of the switched fuzzy systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results.