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Description µ-Tools function Xmath/Xµ equivalent
H
2
norm calculation h2norm h2norm
H
∞
norm calculation hinfnorm hinfnorm
H
2
controller synthesis h2syn h2syn
H
∞
controller synthesis hinfsyn hinfsyn
The major syntactical difference is that the Xµ functions do not return the closed loop
system. This is easily calculated by a subsequent call to starp. The reason for this is
that the D-K iteration changes typically involve a differently weighted closed loop
system in subsequent operations. Having a separate calculation of the closed loop
reduces the potential for confusion.
The µ-Tools function hinffi has no Xmath/Xµ equivalent. This function calculates the
full information H
∞
controller. hinfsyn solves the more general problem and is of more
practical use in controller applications.
A.7 Structured Singular Value (µ) Analysis and Synthesis
The issue of whether or not the frequency domain variable is radian/second or Hertz
arises here. Although this makes no difference to the calculation of µ is affects how the
D scales and ∆ perturbations are interpolated. µ-Tools assumes that the frequency scale
is radians/second. In Xµ the default assumption is Hertz. The reason for this is that
Hertz is the default output of the frequency response calculation freq.Inallcases
where it makes a difference, the user can specify the keyword {!Hertz} to switch the
meaning of the domain.
Calculation of µ
There is a difference in the returned variable format for the Xµ function mu.The
Matlab function returns the D-scale and perturbations in coded vector form. The Xµ
mu function returns both the D scale and its inverse in matrix form. The relevant
functions are summarized below.