# linfn

infinity norm

### Syntax

[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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