具有方差和极点约束的不确定系统鲁棒H∞输出反馈控制

针对一类具有范数有界不确定性的连续系统和二次矩阵不等式区域, 考虑系统具有方差和区域极点约束 的输出反馈控制器设计问题. 为此首先导出闭环系统区域稳定的充分必要条件. 然后用线性矩阵不等式方法给出输出反馈控制器存在的一个充分条件. 在此充分条件下闭环系统是鲁棒区域稳定的且具有H-infinity性能以及当干扰为白噪声信号时其稳态状态方差有限. 接下来用矩阵分解方法给出输出反馈控制器增益矩阵的求解过程. 最后通过一个仿真实例说明本文所提出的控制器设计方法的有效性.

Robust H-infinity output feedback control with variance and pole constraints for time-varying uncertain systems

The design method of robust H-infinity output feedback controller with state variance and regional pole constraints is proposed in this paper for a class of time-varying uncertain systems and a quadratic matrix inequality region. Firstly, a necessary and sufficient condition of regional stable for the closed-loop system is introduced. Secondly, a sufficient condition for the existence of such output feedback controller is derived by means of linear matrix inequality approach. Under the proposed sufficient condition, the closed-loop system is robustly regional stable, possesses H-infinity performance and finite steady state variance when the disturbance is a zero-mean Gaussian white noise process. The gain matrices of the output feedback controller are also constructed by means of the method of matrix decomposition. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller designing method.