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# zpk2ss

Zero pole gain to state space

### Syntax

`S = zpk2ss(sys)`

### Arguments

sys

A linear dynamical system in zero-pole-gain representation (see zpk).

S

The state space representation of sys.

### Description

Converts a zero pole gain representation to state space.

### Examples

```sys = zpk([2;1], [0;-3-%i;-3+%i], 2.5, "c")
typeof(sys)

S = zpk2ss(sys)
typeof(S)```
```--> sys = zpk([2;1], [0;-3-%i;-3+%i], 2.5, "c")
sys  =
(s-2) (s-1)
2.5 -------------
s (s^2+6s+10)

--> typeof(sys)
ans  =
"zpk"

--> S = zpk2ss(sys)
S  =

S(1)  (state-space system:)

"lss"  "A"  "B"  "C"  "D"  "X0"  "dt"

S(2)= A matrix =
0.   1.         -0.3162278
0.  -6.         -3.1622777
0.   3.1622777   0.

S(3)= B matrix =
0.
1.
0.

S(4)= C matrix =
-5.   2.5  -0.7905694

S(5)= D matrix =
0.

S(6)= X0 (initial state) =
0.
0.
0.

S(7)= Time domain =
"c"

--> typeof(S)
ans  =
"state-space"
```

### See Also

• zp2ss — Zero pole gain to state space
• zpk2tf — Zero pole gain to transfer function

### History

 Version Description 6.0 Function added.

### Comments

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 Report an issue << zpk Linear System Representation zpk2tf >>

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