A Generalized Framework of Linear Multivariable Control

4.6 Poles and zeros

The connections between a coprime polynomial fraction description for a strictly proper rational transfer function G(s) and minimal realizations of G(s) can be used to define notions of poles and zeros of G(s) that generalize the familiar notions for scalar transfer functions. In addition we characterize these concepts in terms of response properties of a minimal realization of G(s). For the peer results for discrete time, some translation and modification of these results are required.

Given coprime polynomial fraction descriptions

$\begin{array}{l}\hfill G(s)=N(s)D^{-1}(s)=D_L^{-1}(s)N_L(s),\end{array}$

  (4.68)

it follows from Theorem 4.3.5 that the polynomials ...