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bilin Scilab Group Scilab Function bilin
NAME
bilin - general bilinear transform
CALLING SEQUENCE
[sl1]=bilin(sl,v)
PARAMETERS
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])
EXAMPLE
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)
SEE ALSO
horner, cls2dls
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