On formalism and stability of switched systems-中国Betway体育网页登陆

摘要 Inthispaper,weformulateauniformmathematicalframeworkforstudyingswitchedsystemswithpiecewiselinearpartitionedstatespaceandstatedependentswitching.Basedonknownresultsfromthetheoryofdifferentialinclusions,wedeviseaLyapunovstabilitytheoremsuitableforthisclassofswitchedsystems.Withthis,weproveaLyapunovstabilitytheoremforpiecewiselinearswitchedsystemsbymeansofaconcreteclassofLyapunovfunctions.Contrarytoexistingresultsonthesubject,thestabilitytheoremsinthispaperincludeFilippov(orrelaxed)solutionsandallowinfiniteswitchinginfinitetime.Finally,weshowthatforaclassofpiecewiselinearswitchedsystems,theinertiaofthesystemisnotsufficienttodetermineitsstability.Anumberofexamplesareprovidedtoillustratetheconceptsdiscussedinthispaper.

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On formalism and stability of switched systems

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