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# ss2zp

SIMO state space system to zero pole gain representation

### Syntax

[z,p,k]=ss2zp(S)

### Arguments

S

a single input linear system in state space representation.

z

a matrix, the ith column contains the transmission zeros relative to the ith output.

p

a column vector, the poles of the system

k

a column vector, the ith element contains the gain relative to the ith output.

### Description

Converts a SIMO state space system into zero pole gain representation.

The zeros and gain are computed using the upper triangular Kronecker form (see kroneck) of the matrix pencil

### Examples

a=[ 0.9, 0,   -4.2;
0.2, 0.1,  0.6;
6.4, 0.1,  -4];

b=[-0.1;0;-0.1];
c=[2,0,-2;0,-1,3];
d=[2;0];
S=syslin('c',a,b,c,d);
[z,p,k]=ss2zp(S)

h=ss2tf(S(1,1))
roots(h.num)

### References

A. Emami-Naeini, P. Van Dooren "CComputation of zeros of linear multivariable systems" Automatica. Vol. 18, 1982, p. 415

• trzeros — transmission zeros and normal rank
• systmat — system matrix
• kroneck — Kronecker form of matrix pencil
• zp2ss — Zero pole gain to state space