不确定分布式时滞系统的鲁棒H_∞状态反馈控制

Robust H_∞ statefeedback control for a class of uncertain systems with distributed delay

针对一类不确定分布式时滞系统的鲁棒H∞控制问题,采用线性矩阵不等式的方法通过选择适当的lyapunov函数,得到了自治系统的鲁棒渐进稳定的充分条件。推导出了闭环系统鲁棒渐近稳定的充分条件,并设计了无记忆性H∞状态反馈控制器,使得对于所有允许的不确定性,闭环系统鲁棒渐近稳定且具有给定的H∞性能指标。给出了控制器存在时滞相关的充分条件,且控制器参数能够通过求解线性矩阵不等式得到,对于一个高阶的数值仿真系统,通过对线性矩阵不等式的求解可以得到最优H∞性能指标,及相应不等式的解。仿真证明了该设计方案的有效性。

The problem of robust H∞ controller design for a class of uncertain systems with distributed delay is investigated. The distributed delay is assumed to appear in both the state and controlled output equations. The problem addressed is to design an H∞ controller, such that for all admissible uncertainties, the closed-loop system is robustly asymptotically stable and satisfies a prescribed H∞ performance. A sufficient delay-dependent condition is presented to guarantee the existence of desired controller, which can be constructed by solving a linear matrix inequality （LMI）. By solving a high order numerical system we can get the optimal H∞ performance and the result of the LMI. The effectiveness of the proposed design method is demonstrated by a numerical example.