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
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
|
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA -
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
function [n]=linf(g,eps,tol)
//linf(g,[eps],[tol]) L_infinity norm
// n=sup [sigmax(g(jw)] (sigmax largest singular value).
// w
//-- g is a syslin system.
//-- eps is error tolerance on n.
//-- tol threshold for imaginary axis poles.
// See also: h_norm
//!
if type(g)==1,if norm(g)==0,n=0,return,end,end,
if and(typeof(g)<>['rational','state-space']) then
error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"linf",1))
end
if g.dt<>'c'&g.dt<>[] then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Continuous time system expected.\n"),"linf",1))
end
g.dt='c'
if typeof(g)=='rational' then g=tf2ss(g),end
[lhs,rhs]=argn(0),
select rhs,
case 1 then eps=1e-7,tol=1000*%eps,
case 2 then tol=1000*%eps,
end,
[a,b,c,d]=g(2:5),[t,t]=size(a),
p=ctr_gram(g),q=obs_gram(g);
//Algorithm:
//----------
//1. min , max.
//----------------------------------
[slp,slm]=dtsi(g),
if slp==0 then pp=0,qq=0,tp=1,
pm=p,qm=q,tm=t,
else
if slm==0 then pm=0,qm=0,tm=1,
pp=p,qq=q,tp=t,
else
[tp,tp]=size(slp(2)),[tm,tm]=size(slm(2)),
pp=ctr_gram(slp),qq=obs_gram(slp),
pm=ctr_gram(slm),qm=obs_gram(slm),
end,
end,
hsvp=sqrt(spec(pp*qq)),hsvp=gsort(real(hsvp)),
hsvm=sqrt(spec(pm*qm)),hsvm=gsort(real(hsvm)),
gl=maxi([norm(d),hsvp(tp),hsvm(tm)]),
gu=norm(d)+2*(sum(hsvp)+sum(hsvm)),
//2. binary search
//----------------------
while gu-gl>2*eps*gl,
x=(gl+gu)/2,
r=d'*d-(x*x)*eye(),s=d*d'-(x*x)*eye(),
mx=[a-b/r*d'*c, -x*b/r*b'; ..
x*c'/s*c, -a'+c'*d/r*b'],
mp=abs(real(spec(mx))),mp=mini(mp),
if mp>tol then gu=x, else gl=x, end,
end;
n=(gu+gl)/2
endfunction
|
