National Instruments 370757C-01, NI MATRIX Xmath Robust Control Module L Infinity Norm (linfnorm)

Chapter 3 SystemEvaluation
© National Instruments Corporation 3-3 MATRIXx Xmath Robust Control Module
Figure 3-1. Singular Value Plot
L Infinity Norm (linfnorm)
The L∞ norm of a stable transfer matrix H is defined as:
where is the maximum singular value and H(jω) is the transfer matrix
under consideration.
The L∞ norm of a stable transfer matrix is the maximum of the maximum
singular values over frequency. For example, the highest point of its
singular values plot. Observe that the L∞ norm can be calculated even if His
not stable.
A simple interpretation of the L∞ norm of a stable system can be given as:
where u and y are the input and output of H, respectively. This means that
is the root mean square (RMS) gain of the system: it is the largest
H∞sup σHjω()()=
ωℜ∈
σ
H∞maxRMS y()
RMS u()
--------------------
=
H∞