Algorithms and Software for LMI Problems in Control Introduction
Algorithms and Software for LMI Problems in Control Introduction
Algorithms and Software for LMI Problems in Control Introduction
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Thedeterm<strong>in</strong>antmaximizationproblem Extensions<br />
thefollow<strong>in</strong>g<strong>for</strong>m: theSDP(1),whichwasdiscussed<strong>in</strong>moredetail<strong>in</strong>[76].Thisextensioncanbewritten<strong>in</strong> Intheirsurveyof<strong>LMI</strong>problems<strong>in</strong>control,Boydetal.[3]alsoconsideredanextensionof<br />
m<strong>in</strong>imizebTy�logdet subjecttoC+mXi=1yiAi �D�mXi=1yiBi!<br />
D+mXi=1yiBi0 (15)<br />
<strong>in</strong><strong>for</strong>mation<strong>and</strong>communicationtheory.There<strong>for</strong>ethetheorybeh<strong>in</strong>dtheirsolutionisof <strong>and</strong>(14)areduals.<br />
an<strong>in</strong>terior-po<strong>in</strong>tmethod<strong>for</strong>themaxdet-problemaredescribed<strong>in</strong>[76].<strong>Software</strong><strong>for</strong>solv<strong>in</strong>g great<strong>in</strong>terest,<strong>and</strong>theresult<strong>in</strong>galgorithmshavewideapplication.Alistofapplications<strong>and</strong> Maxdet-problemsarise<strong>in</strong>manyelds,<strong>in</strong>clud<strong>in</strong>gcomputationalgeometry,statistics,<strong>and</strong><br />
maxdet-problemsisavailable<strong>in</strong>[77],<strong>and</strong>hasbeen<strong>in</strong>corporated<strong>in</strong>SDPSOL[68]. Thegeneralizedeigenvaluem<strong>in</strong>imizationproblem<br />
theirmaximumgeneralizedeigenvalue,wecansolvetheoptimizationproblem posewehaveapairofmatrices(A(x);B(x)),bothanefunctionsofx.Inordertom<strong>in</strong>imizeAthirdst<strong>and</strong>ardproblemfrom[3]isthegeneralizedeigenvaluem<strong>in</strong>imizationproblem.Sup- m<strong>in</strong>imizet<br />
3TheproblemwasdenotedCP<strong>in</strong>[3]. subjecttotB(x)�A(x) B(x) 0: 0 (16)<br />
8
Change language