IEEE Trans Cybern. 2014 Dec;44(12):2557-67. doi: 10.1109/TCYB.2014.2310591. Epub 2014 Apr 10.
In this paper, based on the nonmonotonic Lyapunov functions, a new less conservative state feedback controller synthesis method is proposed for a class of discrete time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems. Parallel distributed compensation (PDC) state feedback is employed as the controller structure. Also, a T-S fuzzy observer is designed in a manner similar to state feedback controller design. The observer and the controller can be obtained separately and then combined together to form an output feedback controller by means of the Separation theorem. Both observer and controller are obtained via solving a sequence of linear matrix inequalities. Nonmonotonic Lyapunov method allows the design of controllers for the aforementioned systems where other methods fail. Illustrative examples are presented which show how the proposed method outperforms other methods such as common quadratic, piecewise or non quadratic Lyapunov functions.
本文基于非单调李雅普诺夫函数，针对一类由 Takagi-Sugeno（T-S）模糊系统表示的离散时间非线性系统，提出了一种新的不保守的状态反馈控制器综合方法。采用并行分布补偿（PDC）状态反馈作为控制器结构。同时，类似于状态反馈控制器设计，设计了 T-S 模糊观测器。观测器和控制器可以分别获得，然后通过分离定理组合在一起形成输出反馈控制器。观测器和控制器都是通过求解一系列线性矩阵不等式获得的。非单调李雅普诺夫方法允许为其他方法失败的上述系统设计控制器。给出的实例表明了所提出的方法如何优于其他方法，例如常见的二次、分段或非二次李雅普诺夫函数。
