Tracking Control of Linear Systems

Chapter 6 Nondegenerate matrices

6.1 Nondegenerate and degenerate matrices

For what follows the reader will need the knowledge of definitions and properties of the greatest common (left, right) divisors of the matrix polynomials, of the unimodular matrix polynomials, as well as the knowledge of the conditions for their (left, right) coprimeness (see the books by J. P. Antsaklis and A. N. Michel [8, pp. 526-528, 535-540], C.-T. Chen [29, pp. 591-599] and T. Kailath [198, pp. 373-382]).

A rational matrix function $M(.)=M_D^{-1}(.)M_N(.)\left[M(.)=M_N(.)M_D^{-1}(.)\right]$ is irreducible if, and only if, its polynomial matrices M_D (.) and M_N(.) are (left and/or right) coprime (see C.-T. Chen [29, pp. 591-599] and T. Kailath [198, pp. 373-382]). The greatest ...