多变量连续动态系统的离散化模型参数总和趋Im定理的严格证明
A Rigorious Proof of the Tending-to-Im Theorem for Parameter Sum of the Sampled Model of a Multivariable Continuous System
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摘要: 给出了n阶,r个输入,m个输出的多变量连续动态系统的离散化模型参数总和的具体形式,从中得出了当采样周期h趋于零时,模型参数总和趋于单位阵Im。已经证实本定理对解决处于闭环中全部参数同时进行最小二乘估计十分有用。Abstract: Give the concrete form of the parameter matrix sum of the discretized model of a r-input m-output n-order continuous linear dynamic system with sampling period h. Furthermore, it is proved that the parameter matrix sum of a multivariable discretized system tends to identity matrix, as the sampling period h approaches zero. The theorem has been verified to be very useful in estimating the all parameters of controlled plant in a closed loop via least squares method.