离散系统控制器设计和稳定性分析

Controller Design and Stability Analysis of Time-Discrete Systems

首先给出离散系统模糊状态模型的表示方法，在此基础上给出了一种模糊状态反馈控制器的设计方法，对其稳定性进行了分析，得出了一个确保系统全局稳定的充分条件，同时也给出一种模糊观测器的设计方法，并对其收敛性进行了分析，得出了确保收敛的一个充分条件；最后，利用Ｌｙａ－ｐｕｎｏｖ稳定性理论，分析了基于模糊观测器的反馈控制系统的“分离”特性．

A fuzzy state model for time-discrete systems is presented. Based on the model a controller design method with fuzzy state feedback is given. The stability of the fuzzy systems is analyzed. A design method for fuzzy observers is also given. A sufficient condition which guarantees the convergence of the estimated states to the real states is obtained. Authors then show that a state feedback controller and an observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the Lyapunov method using positive definite matrices. In this sense it is shown that the separation principle holds for Takagi-Sugeno fuzzy systems.