120 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ
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mu analysis of robust performance
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3.7.4 Constructing Rational Perturbations
For simulation purposes it is useful to be able to construct a ratio nal approximation to
the ∆ returned by the µcalculation. The approach is to choose a ∆ at a particular
frequency, for example the one where µis at a maximum, and obtain a MIMO system
which has a frequency response (gain and phase) equal to ∆ at that frequency.
The function for this purpose is function mkpert. The syntax is given below.
pertsys = mkpert(Delta,blk,mubnds)
This function takesas arguments the variables Delta,blk,andmubnds. The meaning of
these is identical to the mu case. The frequency selected for the interpolation is that
where the lower bound (in mubnds) is maximum. Alternatively the user canuse
keywordsto specify a frequencyat which to do the interpolation and specify the norm of
the resulting pertsys.pertsys will be an all-pass system.
Monte-Carlo simulationapproaches require the ability to generate random p erturbations
having the correct block structure. The function for this purpose is randpert and its
usage is illustrated below.