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Zeros and gain of SISO dynamic system


z = zero(sys)
[z,gain] = zero(sys)
[z,gain] = zero(sysarr,J1,...,JN)


z = zero(sys) returns the zeros of the single-input, single-output (SISO) dynamic system model, sys.

[z,gain] = zero(sys) also returns the overall gain of sys.

[z,gain] = zero(sysarr,J1,...,JN) returns the zeros and gain of the model with subscripts J1,...,JN in the model array sysarr.

Input Arguments


SISO dynamic system model.

If sys has internal delays, zero sets all internal delays to zero, creating a zero-order Padé approximation. This approximation ensures that the system has a finite number of zeros. zero returns an error if setting internal delays to zero creates singular algebraic loops.


Array of dynamic system models.


Indices identifying the model sysarr(J1,...,JN) in the array sysarr.

Output Arguments


Column vector containing the locations of zeros in sys. The zero locations are expressed in the reciprocal of the time units of sys. For example, the zeros are in units of 1/minutes if the TimeUnit property of sys is minutes.


Gain of sys (in the zero-pole-gain sense).


collapse all

Create the following transfer function:

H = tf([4.2,0.25,-0.004],[1,9.6,17]);

Calculate the zero locations and overall gain of the transfer function.

[z,gain] = zero(H)
z = 


gain = 4.2000

The zero locations are expressed in radians per second, because the time unit of the transfer function (H.TimeUnit) is seconds.

Change the model time units.

H = chgTimeUnit(H,'minutes');

zero returns locations relative to the new unit.

[z,gain] = zero(H)
z = 


gain = 4.2000


To calculate the transmission zeros of a multi-input, multi-output system, use tzero.

See Also

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Introduced before R2006a