不确定多时滞广义系统的鲁棒H∞控制

研究了一类具有范数有界不确定性和多状态滞后的广义系统的鲁棒H∞控制问题。利用Lyapunov函数方法和线性矩阵不等式工具,首先得到广义闭环系统渐近稳定且具有H∞范数界γ的时滞相关充分条件,然后基于相应的线性矩阵不等式,给出了无记忆H∞状态反馈控制器的设计方法,进一步,通过求解一个凸优化问题得到最优H∞状态反馈控制器。最后,用数值例子说明了该方法的有效性。

Robust H∞ Control for Uncertain Generalized Systems with Multiple Time-delays

The problem of robust H∞ control for a class of uncertain generalized systems with multiple time-delays is discussed. Firstly, based on Lyapunov functional method and linear matrix inequality technique, a delay-dependent sufficient condition is obtained, which ensures that the closed-loop system is asymptotic stable and with H∞ norm bound. Then, a design method for the memoryless state feedback H∞ controller of the system is presented. Furthermore,a design method of the optimal state feedback H∞ controller is obtained by solving a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.