IEEE Trans Cybern. 2016 Aug;46(8):1952-7. doi: 10.1109/TCYB.2015.2458896. Epub 2015 Aug 24.
In this paper, the problem of switching stabilization for a class of switched nonlinear systems is studied by using average dwell time (ADT) switching, where the subsystems are possibly all unstable. First, a new concept of ADT is given, which is different from the traditional definition of ADT. Based on the new proposed switching signals, a sufficient condition of stabilization for switched nonlinear systems with unstable subsystems is derived. Then, the T-S fuzzy modeling approach is applied to represent the underlying nonlinear system to make the obtained condition easily verified. A novel multiple quadratic Lyapunov function approach is also proposed, by which some conditions are provided in terms of a set of linear matrix inequalities to guarantee the derived T-S fuzzy system to be asymptotically stable. Finally, a numerical example is given to demonstrate the effectiveness of our developed results.
本文采用平均驻留时间（ADT）切换研究了一类切换非线性系统的切换稳定化问题，其中子系统可能都是不稳定的。首先，给出了一个新的 ADT 概念，它与传统的 ADT 定义不同。基于新提出的切换信号，推导出了具有不稳定子系统的切换非线性系统稳定化的充分条件。然后，应用 T-S 模糊建模方法来表示基础非线性系统，使得所得到的条件易于验证。还提出了一种新的多二次 Lyapunov 函数方法，通过该方法可以给出一组线性矩阵不等式条件，以保证所得到的 T-S 模糊系统渐近稳定。最后，通过一个数值例子验证了所提出方法的有效性。
