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Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
linfn
infinity norm
Calling Sequence
[x,freq]=linfn(G,PREC,RELTOL,options);
Arguments
- G
is a
syslin
list- PREC
desired relative accuracy on the norm
- RELTOL
relative threshold to decide when an eigenvalue can be considered on the imaginary axis.
- options
available options are
'trace'
or'cond'
- x
is the computed norm.
- freq
vector
Description
Computes the Linf (or Hinf) norm of G
This norm is well-defined as soon as the realization
G=(A,B,C,D)
has no imaginary eigenvalue which is both
controllable and observable.
freq
is a list of the frequencies for which ||G||
is
attained,i.e., such that ||G (j om)|| = ||G||
.
If -1 is in the list, the norm is attained at infinity.
If -2 is in the list, G
is all-pass in some direction so that
||G (j omega)|| = ||G||
for all frequencies omega.
The algorithm follows the paper by G. Robel
(AC-34 pp. 882-884, 1989).
The case D=0
is not treated separately due to superior
accuracy of the general method when (A,B,C)
is nearly
non minimal.
The 'trace'
option traces each bisection step, i.e., displays
the lower and upper bounds and the current test point.
The 'cond'
option estimates a confidence index on the computed
value and issues a warning if computations are
ill-conditioned
In the general case (A
neither stable nor anti-stable),
no upper bound is prespecified.
If by contrast A
is stable or anti stable, lower
and upper bounds are computed using the associated
Lyapunov solutions.
See Also
- h_norm — H-infinity norm
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