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Contents
JózefDuda
Thequadraticfunctionalsforlineartimedelaysystems
Summary
7
Inthismonographarepresentedresultsoftheauthor’sresearchonthe
determinationoftheLyapunovfunctionalsforlinearsystemswithtimedelayand
itsapplicationsintheparametricoptimizationproblem.TheLyapunovquadratic
functionalsareusedtocalculationofavalueofaquadraticperformanceindex
ofqualityintheprocessofparametricoptimizationfortimedelaysystems.The
valueofthatfunctionalattheinitialstateofthetimedelaysystemisequalto
thevalueofaquadraticperformanceindexofquality.Tocalculatethevalueof
aperformanceindexofqualityoneneedstheformulasfortheLyapunovfunctional
coefcients.InthismonographthemethodproposedbyRepin[98]isappliedto
obtaintheLyapunovfunctionals,withcoefcientsgivenbyanalyticalformulas.In
chapter2areconsideredsystemswiththeretardedtypetimedelay.Thismethod
isappliedtothesystemwithonedelay(chapter2.2),tothesystemwithtwo
delays(chapter2.3),totheretardedtypetimedelaysystemwithbothlumpedand
distributeddelay(chapter2.4),tothesystemwitharetardedtypetime-varying
delay(chapter2.5).Inchapter3areconsideredneutralsystems.Repin’smethodis
appliedtotheneutralsystemwithlumpeddelay(chapter3.2),totheneutralsystem
withbothlumpedanddistributeddelay(chapter3.3)andtotheneutralsystem
withatime-varyingdelay(chapter3.4).Inlastyearsamethodofdetermination
ofaLyapunovfunctionalbymeansofLyapunovmatricesisverypopular,seefor
example[66
–
77,79
–
82,89,90,94,100
–
102].Thismethodisappliedtotheparametric
optimizationproblemofretardedtypetimedelaysystembothwithoneandtwo
delays(chapter4)andtotheparametricoptimizationproblemofneutraltypetime
delaysystemforsystemwithoneandtwodelays(chapter5).Theexamplesof
usingoftheLyapunovfunctionalstocalculationoftheperformanceindexvaluein
theparametricoptimizationproblemforlinearsystemswithtimedelayaregiven.
