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
|
.TH linfn 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
linfn - infinity norm
.SH CALLING SEQUENCE
.nf
[x,freq]=linfn(G,PREC,RELTOL,options);
.fi
.SH PARAMETERS
.TP 10
G
: is a \fVsyslin\fR list
.TP
PREC
: desired relative accuracy on the norm
.TP
RELTOL
: relative threshold to decide when an eigenvalue can be
considered on the imaginary axis.
.TP
options
: available options are \fV'trace'\fR or \fV'cond'\fR
.TP
x
is the computed norm.
.TP
freq
: vector
.SH DESCRIPTION
Computes the Linf (or Hinf) norm of \fVG\fR
This norm is well-defined as soon as the realization
\fVG=(A,B,C,D)\fR has no imaginary eigenvalue which is both
controllable and observable.
.LP
\fVfreq\fR is a list of the frequencies for which \fV||G||\fR is
attained,i.e., such that \fV||G (j om)|| = ||G||\fR.
.LP
If -1 is in the list, the norm is attained at infinity.
.LP
If -2 is in the list, \fVG\fR is all-pass in some direction so that
\fV||G (j omega)|| = ||G||\fR for all frequencies omega.
.LP
The algorithm follows the paper by G. Robel
(AC-34 pp. 882-884, 1989).
The case \fVD=0\fR is not treated separately due to superior
accuracy of the general method when \fV(A,B,C)\fR is nearly
non minimal.
.LP
The \fV'trace'\fR option traces each bisection step, i.e., displays
the lower and upper bounds and the current test point.
.LP
The \fV'cond'\fR option estimates a confidence index on the computed
value and issues a warning if computations are
ill-conditioned
.LP
In the general case (\fVA\fR neither stable nor anti-stable),
no upper bound is prespecified.
.LP
If by contrast \fVA\fR is stable or anti stable, lower
and upper bounds are computed using the associated
Lyapunov solutions.
.SH SEE ALSO
h_norm
.SH AUTHOR
P. Gahinet
|
