用频域模型近似多变量系统时的反馈稳定性

Feedback Stability Based on Approximate Frequency-domain Models for Linear Multivariable Systems

本文研究线性多变量系统当其模型不能精确获得时的频域稳定性问题。使用真实系统的近似频域模型，通过线性算子在复频域上的压缩条件，利用系统构模误差矩阵的范数运算得到了其实系统开环逆的范数上界以及近似模型闭环稳定后使实际系统也保持闭环稳定的一个新的充分条件；所得结果亦可应用于开环不稳定最小相位系统。

This paper discusses the problem of frequency-domain stability for linear multivariable systems when their models can not be obtained precisely. By using the approximate frequency-domain model for a real systems, the contraction-mapping condition of linear operator in frequency-domain and some norm of the system modelling error, a sufficient condition is developed which stabilizes the real system and its approximate model closed-loop as well as a new norm upper-bound which is real system open-loop inverse matrix is obtained. The new criterion is applicable to systems with open-loop unstable minimum-phase systems.