linfn

[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