1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
|
function [sl]=tf2ss(h)
// Transfer function to state-space.
//Syntax : sl=tf2ss(h)
// h = transfer matrix
// sl = linear system in state-space representation (syslin list)
//!
// Copyright INRIA
if type(h)<=2 then
sl=syslin([],[],[],[],h);return;
end
[num,den]=h(2:3);
//
[nd,md]=size(den)
a=[];b=[];c=[];d=[];n1=0; // s=[]
for k=1:md
for l=1:nd
[r,q]=pdiv(num(l,k),den(l,k));
dk(l)=q;
num(l,k)=r;
end
if nd<>1 then [nk,pp]=cmndred(num(:,k),den(:,k));
else
pp=den(k);nk=num(k);
end;
slk=cont_frm(nk,pp);//
[ak,bk,ck,dk1]=slk(2:5);
// [s sk]
[n2,m2]=size(bk);
if n2<>0 then
a(n1+1:n1+n2,n1+1:n1+n2)=ak;
b(n1+1:n1+n2,k)=bk;
c=[c ck];
n1=n1+n2;
else
if n1<>0 then b(n1,k)=0;end
end;
d=[d dk];
end;
if degree(d)==0 then d=coeff(d),end
if n1<>0 then
nrmb=norm(b,1);nrmc=norm(c,1);fact=sqrt(nrmc*nrmb);
b=b*fact/nrmb;c=c*fact/nrmc;
[a,u]=balanc(a);c=c*u;b=u\b;
[no,u]=contr(a',c');
u=u(:,1:no);
a=u'*a*u;b=u'*b;c=c*u;
[a,u]=balanc(a);c=c*u;b=u\b;
sl=syslin(h(4),a,b,c,d);
else
sl=syslin(h(4),[],[],[],d)
end
|
