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# 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.

### Comments

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