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<title>MvTools Help : Synthesis ---> MU</title>
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<div class=Section1>
<p align=center style='text-align:center'><span lang=EN-US><img width=371
height=51 id="_x0000_i1025" src="Immagini\logosyn.jpg"></span></p>
<p align=center style='text-align:center'><span lang=EN-US><a
href="HelpDeskmvt.htm" title=" MVTOOLS HELP DESK "><b><i>MvTools Help Desk</i></b></a></span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=536 height=5 id="_x0000_i1026" src="Immagini\riga.gif"></span></p>
<p align=center style='text-align:center'><b><u><span lang=EN-US
style='font-size:13.5pt;color:red'>MU<o:p></o:p></span></u></b></p>
<p align=center style='text-align:center'><span lang=EN-US>(Output Feedback)</span></p>
<p style='text-align:justify'><span lang=EN-US>The MU synthesis <a
href="biblo.htm#b10" title=" REFERENCE ">[10]</a> manages the problem of robust
stability in front of structured uncertainties. It's important to remember that
any nominal (or current) model is obtained by theoretical or identification
methods and certainly differs in behavior from the corresponding actual system;
all the differences between these two plants are named system uncertainties or
modeling errors and the most important objective in MU control design is to
find a controller that not only stabilizes the nominal model, but which must
also stabilize a family of systems which exist in a uncertainty region around
the nominal model.</span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>Using a LFT (Linear Fractional Transformation) <a href="biblo.htm#b7"
title=" REFERENCE ">[7]</a> it's possible to obtain the following </span><span
lang=EN-US style='color:green'>general structure</span><span lang=EN-US> in
which any linear interconnection of inputs (v,u), outputs (e,y) and
uncertainties (</span><span lang=EN-US style='font-family:Symbol'>D</span><span
lang=EN-US>) may be rearranged: </span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=325 height=175 id="_x0000_i1027" src="Immagini\synmu00.gif"></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>where P</span><span lang=EN-US style='font-size:10.0pt'>(s)</span><span
lang=EN-US> represents the generalized plant (nominal model plus all the
necessary weighting functions) and K</span><span lang=EN-US style='font-size:
10.0pt'>(s)</span><span lang=EN-US> the controller; v</span><span lang=EN-US
style='font-size:10.0pt'>(s)</span><span lang=EN-US> is a vector of exogenous
inputs such as reference commands, disturbance and noise, e</span><span
lang=EN-US style='font-size:10.0pt'>(s)</span><span lang=EN-US> is a vector of
error signal to be kept small, y</span><span lang=EN-US style='font-size:10.0pt'>(s)</span><span
lang=EN-US> is a vector of sensor measurements, u</span><span lang=EN-US
style='font-size:10.0pt'>(s)</span><span lang=EN-US> is a vector of control
signals and the uncertainty </span><span lang=EN-US style='font-family:Symbol'>D</span><span
lang=EN-US> is assumed to be </span><span lang=EN-US style='color:red'>structured</span><span
lang=EN-US> as follow</span></p>
<p align=center style='text-align:center'><span lang=EN-US style='font-size:
10.0pt;font-family:Symbol'>(1) <span style='mso-tab-count:1'>牋牋牋牋 </span></span><span
lang=EN-US style='font-family:Symbol;color:red'>D</span><span lang=EN-US
style='color:red'> = { diag( </span><span lang=EN-US style='font-family:Symbol;
color:red'>D</span><span lang=EN-US style='font-size:7.5pt;color:red'>1 </span><span
lang=EN-US style='color:red'>, </span><span lang=EN-US style='font-family:Symbol;
color:red'>D</span><span lang=EN-US style='font-size:7.5pt;color:red'>2 </span><span
lang=EN-US style='color:red'>,</span><span lang=EN-US style='font-size:7.5pt;
color:red'> </span><span lang=EN-US style='color:red'>..., </span><span
lang=EN-US style='font-family:Symbol;color:red'>D</span><span lang=EN-US
style='font-size:7.5pt;color:red'>n</span><span lang=EN-US style='color:red'> )
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