不确定离散非线性系统的模糊控制

A New Approach to Quadratic Stabilization of Discrete Uncertain Nonlinear System

针对状态不完全可测的一类不确定离散非线性系统,基于状态观测器研究其镇定问题.采用T-S模型对非线性系统进行建模,根据李雅普诺夫稳定性理论,采用线性矩阵不等式(LMI)的形式,利用分散化并行分布补偿(PDC)的方法和新条件,设计了基于观测器的控制器,给出了实现该非线性系统镇定的充分条件.并通过数值仿真对提出的方法进行了验证,仿真结果表明了该方法的正确性.

For the quadratic stabilization problem of a class of discrete - time nonlinear system with parametric uncertainties, the problem of design an controller based on state observer is considered. The Takagi- Sugeno （ T- S） fuzzy model was adopted for fuzzy modeling of the sys- tem. According to Lyapunov stability theory, the scheme of decentralized PDC （ Parallel Distributed Compensation） fuzzy control was used to design controller based on a new approach in the form of LMI. Besides, the sufficient condition that ensures quadratic stabilization of the system was derived. The conclusion was tested by numerical simulation which proves the correctness of the conclusion.