A Rigorious Proof of the Tending-to-I_m Theorem for Parameter Sum of the Sampled Model of a Multivariable Continuous System

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.