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# zpk

Zero pole gain system representation

### Syntax

S=zpk(Z,P,K,dt)

S=zpk(z,p,k,dt))

S=zpk(sys))

### Arguments

- Z
a m by n cell of real or complex vectors, Z{i,j} is the transmission zeros of the transfer from the the jth intput to the ith output.

- P
a m by n cell of real or complex vectors, P{i,j} is the poles of the transfer from the the jth intput to the ith output.

- K
a m by n matrix of real numbers, K(i,j) is the gain of the transfer from the the jth intput to the ith output.

- z
a real or complex vector, the transmission zeros of the siso transfer function.

- p
a real or complex vector, the poles of the siso transfer function.

- k
a real scalar, the gain of the siso transfer function.

- dt
a character string with possible values "c" or "d", [] or a real positive scalar, the system time domain (see syslin).

- sys
A linear dynamical system in transfer function or state spece representation (see syslin).

- S
a mlist with the fields Z , P, K and dt.

- Z
a m by n cell array of real or complex vectors, S.Z{i,j} contains the zeros of the transfer from the the jth intput to the ith output

- P
a m by n cell array of real or complex vectors, S.P{i,j} contains the poles of the transfer from the the jth intput to the ith output

- K
a m by n matrix of real numbers, S.K(i,j) is the gain of the transfer from the the jth intput to the ith output. output.

- dt
a positive scalar or "c" or "d" the time domain

### Description

`S=zpk(Z,P,K,dt)`

forms the multi-input,
multi-output zero pole gain system representation given the
cell arrays of the transmission zeros,poles and gain.

`S=zpk(z,p,k,dt)`

forms the single-input,
single output zero pole gain system representation given the
vecteors of the transmission zeros and poles and the scalar
gain.

`S=zpk(sys)`

converts the system
representation into a zero-pole-gain representation.

The poles and zeros of each transfer function are sorted in decreasing order of the real part.

Most functions and operations than can act on state-space or rational transfer function representations can be also applied to zero-pole-gain representations.

### Examples

//Form system from zeros, poles and gain //SISO case z11=[1 -0.5];p11=[-3+2*%i -3-2*%i -2];k11=1; S11=zpk(z11,p11,k11,"c") //MIMO case z21=0.3;p21=[-3+2*%i -3-2*%i];k21=1.5; S21=zpk(z21,p21,k21,"c") S=zpk({z11 [];z21 1},{p11,0;p21 -3},[k11 1;k21 1],"c") //system representation conversion h=syslin("c",5*(%s^2+2*%s+1)/(%s^2-4)) sh=zpk(h) //operations with zpk representations S(1,:) S' S(1,1)=sh sh*S11 sh./S11

### See Also

### History

Version | Description |

6.0 | Function added. |

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