δ算子的输出反馈H_2最优控制

Output feedback H_2 optimal controller design based on δ operator

对基于δ算子描述下的离散系统,分析证明了存在输出反馈控制器使闭环系统内稳定且满足从w到z的传递矩阵Tzw的H2-范数最小的充要条件,得到了两个基于δ算子的Riccati方程,并给出了连续系统、z变换所得到的离散系统和δ算子所描述系统三者的H2控制问题的比较。结果表明,当采样周期很小时,采用δ算子来离散化连续系统,其系统的性能更趋于连续状态。

The problem of the discrete-time system described by δ operator in the presence of an output feedback controller is analyzed and proved. This controller makes the closed-loop system internally stable and the sufficient and necessary condition for minimum H_2-norm belonging to the transfer matrix T_(zw) is satisfied. Two Riccati formulae based on δ operator are deduced. The H_2 problems for continuous-time systems, Z operator models and δ operator models are investigated respectively. The results show that the characteristics of discrete systems described by δ operator are closer to those of continuous systems, especially when sampling period approaches zero.