bilin

general bilinear transform

Calling Sequence

[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)

See Also

• horner polynomial/rational evaluation
• cls2dls bilinear transform