minreal (Control System Toolbox)

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 transfer 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)

specifies the 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.