This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# TransferFunctionPoles

 TransferFunctionPoles[tf] gives a matrix of roots of the denominators in the TransferFunctionModel object tf.
The poles of a notch filter:
The poles for specific values of damping ratio and natural frequency:
The poles of a MIMO system are the poles of the elements of the transfer function:
The poles of a notch filter:
 Out[1]=
The poles for specific values of damping ratio and natural frequency:
 Out[2]=

The poles of a MIMO system are the poles of the elements of the transfer function:
 Out[1]=
 Scope   (4)
The poles of a fourth-order Butterworth filter:
They lie on the unit circle:
The poles of a tenth-order Bessel filter:
The poles of a discrete-time second-order system:
The system is stable because the poles lie within the unit circle:
The poles of the elements of a MIMO system:
 Applications   (1)
Use TransferFunctionPoles to determine if a system is asymptotically stable:
For a SISO system, the poles of the transfer function are the eigenvalues of its state matrix:
The poles determine the natural response of a system:
The exponentials in the response are the real parts of the poles:
The root locus plot gives the closed-loop poles of the transfer function as any parameter is varied:
A stable third-order system can be better approximated by a second-order system if the third pole is further to the left in the left-half plane:
New in 8