多时滞非线性系统的H_∞控制——线性矩阵不等式法

H-Infinite Controller for Nonlinear Systems with Multiple Time Delay-Linear Matrix Inequality Method

为得到关于非线性多时滞系统的更具一般性的结论,利用目前广泛使用的线性矩阵不等式方法研究了不确定有界的多时滞非线性系统的任意阶鲁棒H∞输出反馈控制器的设计问题,给出了该类问题有解的充分条件,同时设计了控制器.该方法的要旨在于只要相应的矩阵不等式存在正定解,就能够设计任意阶的H∞输出反馈控制器.典型算例说明了此类控制律的设计步骤,仿真结果表明该方法对干扰输入具有较强的抑制能力.

To obtain more general results concerning nonlinear systems with multiple time delay than those in the previous literature, the robust control problems are solved by the linear matrix inequality (LMI) approach widely used recently. The H-infinite output feedback control problems are discussed for a class of uncertain nonlinear systems with multiple state delay time when the uncertainty is bounded. The sufficient conditions for the existence of H-infinite controllers are presented and the controller is constructed simultaneously. It is pointed out that provided the relevant LMIS are solvable, the output feedback control law of any order can be designed. The designing procedure of the proposed controller is summarized through an example. Simulation results indicate that this kind of controller can attenuate disturbances effectively.