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A. TRANSLATION BETWEEN MATLAB µ-TOOLS AND Xµ 401
Description µ-Tools function Xmath/Xµ equivalent
structured singular value mu mu
D scale decoding unwrapd not required
perturbation decoding unwrapp not required
block norm calculations blknorm blknorm
rational perturbation dypert mkpert
random perturbations randel randpert
In the Xµ mu function, only the default options of the µ-Tools mu calculations are
available. In other words, a power iteration, with several random restarts, is used for the
lower bound. The upper bound calculation uses an Osborne balancing method and
enhances this with the Perron vector method for problems with less than 10 blocks.
These methods have been found to be appropriate for the vast majority of practically
motivated problems.
New algorithms for these calculations are currently under development. The most
significant enhancement is the ability to calculate µ with respect to structures which
include real valued blocks. Because of the development effort in this direction, a wide
range of calculation options were not provided for the current Xµ mu function.
The scalar × identity block structure is not currently supported in the Xµ mu function.
It will be included in the revised version discussed above.
The D-K Iteration
There is a significant difference in the way that Xµ handles the D-K iteration. The D
scales are not incrementally factored into the previous iteration D-scales. Consider the
initial design interconnection structure to be ic.AnH
∞
design will produce the first
controller: k1, using a function call like the following.
k1 = hinfsyn(ic,nmeas,ncon,gamma)
The closed loop system, obtained via
g1 = starp(ic,k1)
is then analyzed with mu. The typical function call is: