Contribution à l’estimation et à la commande des systèmes non linéaires

Abstract

Exploring theobservationandestimationofnon-linearsystems,particularlythose representedbyTakagi-Sugenofuzzymulti-systems,thisresearchaddressesthe significantchallengesinmodelingandcreatinganobserverforsuchsystems.Itadopts a multi-modelapproachandemploysnon-linearsectordecompositiontotransformthese systems intoapolytopeform,facilitatingthedevelopmentofarobustobserverthatcan accurately reconstructboththesystem’sstatesanditsunknowninputsundervarious conditions. Thestudycontraststraditionalquadraticapproacheswithaninnovativenon- quadratic methodthatusesaline-integralLyapunovfunctionfortheestimationofboth state andunknowninputs.Thismethod,inconjunctionwithaspeciallydesignedob- server,resultsinlinearmatrixinequalityconditions,providingamorestraightforward solution comparedtothecomplexbilinearmatrixinequalitycommonlyassociatedwith TS fuzzysystems.Notably,thisapproachdemonstratesreducedconservatism,thereby enhancing itseffectivenessandreliability.Additionally,theresearchinvestigatesstate and unknowninputestimationfornon-linearsystemsusingTSfuzzysystemsinscenarios where premisevariablesareunmeasurable,anditincludespracticalexamplestoillustrate the effectivenessoftheproposedmethods.