linfn

Scilab Function
Last update : 25/04/2007

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 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` ,

### Author

P. Gahinet