User`s guide

minreal
11-140
11minreal
Purpose Minimal realization or pole-zero cancellation
Syntax sysr = minreal(sys)
sysr = minreal(sys,tol)
Description sysr = minreal(sys) eliminates uncontrollable or unobservable state in
state-space models, or cancels pole-zero pairs in t ransfer functions or
zero-pole-gain models. The output
sysr has minimal order and the same
response characteristics as the original model
sys.
sysr = minreal(sys,tol) specifiesthe tolerance used for state elimination or
pole-zero cancellation. The default value is
tol = sqrt(eps) and increasing
this tolerance forces additional cancellations.
Example The commands
g = zpk([],1,1)
h = tf([2 1],[1 0])
cloop = inv(1+g*h) * g
produce the nonminimal zero-pole-gain model by typing cloop.
Zero/pole/gain:
s (s–1)
-------------------
(s–1) (s^2 + s + 1)
To cancel the pole-zero pair at , type
cloop = minreal(cloop)
and MATLAB returns
Zero/pole/gain:
s
-------------
(s^2 + s + 1)
Algorithm Pole-zero cancellation is a straightforward search through the poles and zeros
looking for matches that are within tolerance. Transfer functions are first
converted to zero-pole-gain form.
s 1
=