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totheretardedtypetimedelaysystemwithbothlumpedanddistributeddelay
(chapter2.4),tothesystemwitharetardedtypetime-varyingdelay(chapter2.5).In
chapter3.areconsideredneutralsystems.Repin’smethodisappliedtotheneutral
systemwithlumpeddelay(chapter3.2),totheneutralsystemwithbothlumped
anddistributeddelay(chapter3.3)andtotheneutralsystemwithatime-varying
delay(chapter3.4).InlastyearsamethodofdeterminationofaLyapunovfunctional
bymeansofLyapunovmatricesisverypopular,seeforexample[66
–
82,89,90,94,
100
–
102].Thismethodisappliedtotheparametricoptimizationproblemofretarded
typetimedelaysystembothwithoneandtwodelays(chapter4),totheparametric
optimizationproblemofneutraltypetimedelaysystemforsystemwithoneandtwo
delays(chapter5).TheexamplesofusingoftheLyapunovfunctionalstocalculation
oftheperformanceindexvalueintheparametricoptimizationproblemforlinear
systemswithatimedelayaregiven.
Iwouldliketothankeditorialreviewersofthismonograph:prof.Wojciech
MitkowskifromAGHUniversityofScienceandTechnologyandprof.JerzyKlamka
fromSilesianUniversityofTechnology,fortheirmanycommentsandsuggestions,
whichhadimprovedthiswork.
