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Chapter 3 System Evaluation
© 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 H is
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 σ Hjω()()=
ωℜ∈
σ
H
∞
max
RMS y()
RMS u()
--------------------
=
H
∞