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Ajuda do Scilab >> CACSD > Model Transformation > bilin

# bilin

general bilinear transform

### Syntax

`[sl1]=bilin(sl,v)`

### Arguments

sl,sl1

linear systems (`syslin` lists)

v

real vector with 4 entries (`v=[a,b,c,d]`)

### Description

Given a linear system in state space form, `sl=syslin(dom,A,B,C,D)` (`syslin` list), `sl1=bilin(sl,v)` returns in `sl1` a linear system with matrices `[A1,B1,C1,D1]` such that the transfer function `H1(s)=C1*inv(s*eye()-A1)*B1+D1` is obtained from `H(z)=C*inv(z*eye()-A)*B+D` by replacing `z` by `z=(a*s+b)/(c*s+d)`. One has `w=bilin(bilin(w,[a,b,c,d]),[d,-b,-c,a])`

### Examples

```s=poly(0,'s');z=poly(0,'z');
w=ssrand(1,1,3);
wtf=ss2tf(w);v=[2,3,-1,4];a=v(1);b=v(2);c=v(3);d=v(4);
[horner(wtf,(a*z+b)/(c*z+d)),ss2tf(bilin(w,[a,b,c,d]))]
clean(ss2tf(bilin(bilin(w,[a,b,c,d]),[d,-b,-c,a]))-wtf)```

• horner — avaliação polinomial/racional
• cls2dls — bilinear transform
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