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A Generalized Framework of Linear Multivariable Control by Liansheng Tan

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7

Determination of finite and infinite frequency structure of a rational matrix

Abstract

The finite and infinite frequency structures of a rational matrix are fundamental to system analysis and design. The classical methods of determining them are not stable in numerical computations, because the methods are based on unimodular matrix transformations, which result in an extraordinarily large number of polynomial manipulations.

In this chapter a novel method is developed that determines the finite and infinite frequency structure of any rational matrix. For a polynomial matrix, a natural relationship between the rank information of the Toeplitz matrices and the number of the corresponding irreducible elementary divisors in its Smith form is ...

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