gives a matrix of roots of the numerators in the TransferFunctionModel tfm.


only gives the roots inside the region reg on the complex plane.


  • A rectangular region reg can be given as {{remin,remax},{immin,immax}}.
  • The default region is the entire complex plane.


open allclose all

Basic Examples  (3)

Compute the zeros for a SISO system:

Zeros for a MIMO system:

Time-delay systems may have infinite poles:

Get only the values within a square about the origin:

Scope  (5)

The zeros of a SISO system:

The zeros of a MIMO system:

Compute the zeros of a inverted pendulum model:

The zeros of a system with parallel subsystems:

They are different from the zeros of the individual subsystems:

The zeros of a time-delay system in a square around the origin:

The zeros trace out paths on the complex plane:

Applications  (3)

Compute the zeros of a PID controller:

A function to create pole-zero plots:

Find the zeros of the time-delay system near the origin:

Create a delay-free approximation using the poles:

Compare step responses of the time-delay system and the delay-free approximation:

Properties & Relations  (3)

For SISO systems, the zeros block the transmission of specific input signals:

The steady-state response of the system to Sin[0.5 t] is zero:

The response to Sin[5 t] does not go to zero:

A damped second-order system with a minimum-phase zero:

The rise time decreases and the overshoot increases as the zero moves away from the poles:

The response of a system with nonminimum-phase zeros starts out in the reverse direction:

A discrete-time, nonminimum-phase system:

Possible Issues  (1)

TransferFunctionZeros may not find solutions for time-delay systems:

Specify a region:

Plot the poles:

Wolfram Research (2010), TransferFunctionZeros, Wolfram Language function, (updated 2012).


Wolfram Research (2010), TransferFunctionZeros, Wolfram Language function, (updated 2012).


Wolfram Language. 2010. "TransferFunctionZeros." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012.


Wolfram Language. (2010). TransferFunctionZeros. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_transferfunctionzeros, author="Wolfram Research", title="{TransferFunctionZeros}", year="2012", howpublished="\url{}", note=[Accessed: 25-June-2024 ]}


@online{reference.wolfram_2024_transferfunctionzeros, organization={Wolfram Research}, title={TransferFunctionZeros}, year={2012}, url={}, note=[Accessed: 25-June-2024 ]}