Systems using Low Gain Homogeneous

Thispaperexamines theresult ofan output feedback stabilization methodforthecontrol offeed- forwardhomogeneous nonlinear systems withunmeasur- ablestates. Thefeedforward system ismadeup ofa nominalplant whichisdescribed bya chainofodd powerintegrators andcoupled withhigh ordernonlinear functions. Thesenonlinear functions areassumedtobe boundedbyfunctions withhomogeneous dilations. By making useoftheadding apowerintegrator technique in combination withhomogeneous system theory, anobserver andcontroller isimplemented whichcancompensate for thehigh orderhomogeneous functions ofthefeedforward system using only themeasured state. Thisisaccomplished through theuse ofa lowgainscaling factor, which whenappropriately chosen, willdominate thehigh order nonlinearities. Thesignificance ofthisresult isthatlittle information aboutthenonlinear system isrequired to stabilize thissystem. I.INTRODUCTION Theissue ofstabilizing feedforward systems byoutput feedback isa verypractical problem since inmany applications only theoutput ofthesystem isavailable. Unfortunately, this problem isexceptionally challenging incontrast tolower-triangular systems. Thedifficulty in dealing withtheglobal output feedback control problem isduetothestructural obstacle inherent infeedforward system. Ingeneral, thesolvability ofthestate feedback stabilization doesnotimply thesolvability oftheoutput feedback stabilization. Thestabilization offeedforward systems isaninter- esting problem andhasattracted agreat dealofattention. Thefeedforward (also called upper-triangular) system represents animportant class ofnonlinear systems which includes suchproblems asthe"Ball andBeam"system and"rotating pendulum" system. Tosolvethestabi- lization problem, a noveldesign methodusing nested