最小多项式矩阵与线性多变量系统(Ⅱ)

Minimal Polynomial Matrix and Linear Multivariable System(Ⅱ)

摘要: 本文之(Ⅰ)^[8]是关于最小多项式矩阵的理论;其(Ⅱ)是关于这一理论在线性多变量系统中的应用.在本部分的第一节中,我们利用(Ⅰ)中的理论,详细地讨论线性多变量系统输入问题的一些结果.在第二节中,利用对偶性,我们给出行n.p.m.及行生成组等概念,并讨论线性多变量系统输出问题的某些结果.在第三节中.我们讨论化状态空间型为多项式矩阵型的方法.在第四节中,我们讨论这一问题的反问题,即化多项式矩阵型为状态空间型的问题.为说明这些理论和方法,我们给出一些有趣的例子.

Abstract: Part(Ⅰ) of this work is on the theory of minimal polynomial matrix and Part(Ⅱ) is on the applications of this theory to linear multivariable systems.In I of this part, using the theory in Part(Ⅰ), some results about input part of a linear multivariable system are discussed in detail and in Ⅱ, using duality properties, the concepts about row n.p.m.and row generating system, etc. are given, and some results about output part of linear multivariable system are discussed, too. In Ⅲ, we discuss the approach which can give the polynomial model with less dimension from the state-space modeland in Ⅳ we discuss tha inverse of the problem to give the state-space model from the polynomial model. Some interesting examples are given to explain the theory and the approach.

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