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linfn(1) Scilab Function linfn(1)
NAME
linfn - infinity norm
CALLING SEQUENCE
[x,freq]=linfn(G,PREC,RELTOL,options);
PARAMETERS
G : is a syslin list
PREC : desired relative accuracy on the norm
RELTOL : relative threshold to decide when an eigenvalue can be con-
sidered 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 con-
trollable 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 com-
puted using the associated Lyapunov solutions.
SEE ALSO
h_norm
AUTHOR
P. Gahinet
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