# zpk

Constructs a zero, pole, gain model.

## Syntax

SYS = zpk()

SYS = zpk('s')

SYS = zpk('z', Ts)

SYS = zpk(Z, P, K)

SYS = zpk(Z, P, K, Ts)

## Inputs

`Z`- A vector; zeros of the system.
`P`- A vector; poles of the system.
`K`- A scalar; gains of the system.
`Ts`- Sampling time (in seconds).

## Outputs

- SYS
- A zero, pole, gain model (a table).

## Examples

`sys = zpk('s')`

`sys = object [
DisplayFormat: roots
TimeUnit: seconds
ts: 0
Variable: s
k: 1
p:
{
[1,1] p = [Matrix] 0 x 1
type: ZeroPoleGainModel
z:
{
[1,1] z = 0
]`

`sys = zpk([0 -3], [-3,-3+i,-1-i], 8, 9)`

`sys = object [
DisplayFormat: roots
TimeUnit: seconds
ts: 9
Variable: s
k: 8
p:
{
[1,1] p = [Matrix] 1 x 3
-3 + 0i -3 + 1i -1 - 1i
type: ZeroPoleGainModel
z:
{
[1,1] z = [Matrix] 1 x 2
0 -3
]`

`sys = zpk([], [], 7)`

`sys = object [
DisplayFormat: roots
TimeUnit: seconds
ts: -2
Variable: s
k: 7
p:
{
[1,1] p = [Matrix] 0 x 1
type: ZeroPoleGainModel
z:
{
[1,1] z = [Matrix] 0 x 1
]`

## Comments

This generates a zero-pole-gain (ZPK) model.