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# des2ss

descriptor to state-space

### Calling Sequence

```[Sl]=des2ss(A,B,C,D,E [,tol])
[Sl]=des2ss(Des)```

### Arguments

A,B,C,D,E

real matrices of appropriate dimensions

Des

list

Sl

`syslin` list

tol

real parameter (threshold) (default value `100*%eps`).

### Description

Descriptor to state-space transform.

`Sl=des2ss(A,B,C,D,E)` returns a linear system `Sl` equivalent to the descriptor system `(E,A,B,C,D)`.

For index one `(E,A)` pencil, explicit formula is used and for higher index pencils `rowshuff` is used.

`Sl=des2ss(Des)` with `Des=list('des',A,B,C,D,E)` returns a linear system `Sl` in state-space form with possibly a polynomial `D` matrix.

A generalized Leverrier algorithm is used.

### Examples

```s=poly(0,'s');G=[1/(s-1),s;1,2/s^3];
S1=tf2des(G);S2=tf2des(G,"withD");
W1=des2ss(S1);W2=des2ss(S2);
clean(ss2tf(W1))
clean(ss2tf(W2))```

### See Also

• des2tf — descriptor to transfer function conversion
• glever — inverse of matrix pencil
• rowshuff — shuffle algorithm

### Comments

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