极点互异的真有理传递函数阵的最小实现

The Minimum Realization of the Rational Transfer Function Matrix with Distinct Poles

每个真有理传递函数矩阵G(s)均具有有限维、线性、非时变动态方程的实现,从而可在计算机上仿真。G(s)的最小实现必定是能控能观的动态方程。总的看来,求G(s)的"最小实现"有两种方法:一种是用Hankel矩阵求最小实现的直接方法;另一种是间接法,即先建立能控型(能观型)实现,再从中消去不能观(不能控)状态,从而得到一个既能控、又能观的实现。当真有理函数矩阵的极点相异时,此时可使用本文所叙的方法求解,这种方法在大学教材中很少涉及,而且对于这个定理的必要与充分条件皆未做出证明。

Every rational transfer function matrix G（s） has its realization of the finite dimensional, linear, non-variant dynamic equation so as to be simulated on computer. The minimum realization of G（s） must be the controllable and observable dynamic equation. In summary, two calculating methods about the minimum realization of G（s） are introduced. One is the direct method of finding Hankel Matrix; the other is the indirect method of establishing first controllable （observable） realization, then cancelling the unobservable （uncontrollable） state, and obtaining the controllable and observable realization. If the poles of the rational transfer matrix are distinct, this paper introduces another calculating method and principle. And this is seldom concerned on the current textbook, the necessary and sufficient condition of this principle are not proved either.