Chapter 3 SystemEvaluation
MATRIXx Xmath Robust Control Module 3-4 ni.com
factor by which the RMS value of a signal flowing through H can be
increased.
By comparison, the H2 norm is defined as:
This norm can be interpreted as the RMS value of the output when the input
is unit intensity white noise. It can be computed in Xmath using the rms( )
function.
For discrete-time systems with a stable H,
where is the maximum singular value and H(ejω) is the transfer matrix
under consideration.

linfnorm( )

[sigma, vOMEGA] = linfnorm( Sys, {tol,maxiter} )
The linfnorm( ) function computes the L∞ norm of a dynamic system
using a quadratically convergent algorithm. The linfnorm( ) function
relies on eigenvalue calculations of a Hamiltonian matrix with twice as
many states as Sys and, consequently, may be unreliable for large systems.
A singular value plot created with svplot( )can be used as an alternative
in these cases. Refer to the Singular Value Bode Plots section.
• The keyword tol controls the required relative accuracy. The default
is 0.01. maxiter is the maximum number of iterations. The default
is 15.
• If the maximum norm is found at ω = ∞, linfnorm( ) returns:
vOMEGA = Infinity
sigma = gain at infinity.
H2
1
2π
------ σiHjω()()
2
i1=
k
∑
∞–
∞
∫
=dw
H∞
max
ωππ,–()∈σHejω
()()=
σ