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# des2tf

descriptor to transfer function conversion

### Syntax

```S = des2tf(sl)
[Bfs, Bis, chis] = des2tf(sl)```

### Arguments

sl

list (linear system in descriptor form)

Bfs, Bis

two polynomial matrices

chis

polynomial

S

rational matrix

### Description

Given the linear system in descriptor form i.e. `Sl=list('des',A,B,C,D,E)`, `des2tf` converts `sl` into its transfer function representation:

`S=C*(s*E-A)^(-1)*B+D`

Called with 3 outputs arguments `des2tf` returns `Bfs` and `Bis` two polynomial matrices, and `chis` polynomial such that:

`S=Bfs/chis - Bis`

`chis` is the determinant of `(s*E-A)` (up to a xcative constant);

### Examples

```s=poly(0,'s');
G=[1/(s+1),s;1+s^2,3*s^3];
Descrip=tf2des(G);Tf1=des2tf(Descrip)
Descrip2=tf2des(G,"withD");Tf2=des2tf(Descrip2)
[A,B,C,D,E]=Descrip2(2:6);Tf3=C*inv(s*E-A)*B+D```

• glever — inverse of matrix pencil
• pol2des — polynomial matrix to descriptor form
• tf2des — transfer function to descriptor
• ss2tf — conversion from state-space to transfer function
• des2ss — descriptor to state-space
• rowshuff — shuffle algorithm