Page - (000088) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

84 10 Nonlinearity Khalil 2002).Once the linearized system is obtained, onemay apply linear design andanalysis techniques to studyor toalter the systemdynamics. Feedbacklinearizationdependsonanaccuratemodelof thedynamics.Forexam- ple, if theactualmodel is x˙=ax2+u, and the feedback linearization is takenasu=−kx−x2 under theassumption that a=1, then theclosed-loopsystemis x˙=−kx+(a−1)x2. If the truevalueof theparameter isa=2, then the feedback systemhasdynamics x˙=−kx+x2,which isunstable for x> k. Thisexampleshows that feedback linearization isnot robust tomodeluncertain- ties.The followingchapter discusses an alternativemethod that canprovide robust feedbackcontrol fornonlinear systems. OpenAccess This chapter is licensed under the terms of theCreativeCommonsAttribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation,distributionandreproduction inanymediumorformat,as longasyougiveappropriate credit to theoriginal author(s) and thesource,providea link to theCreativeCommons licenseand indicate if changesweremade. The images or other third partymaterial in this chapter are included in the chapter’sCreative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter’s Creative Commons license and your intended use is not permitted by statutory regulationorexceeds thepermitteduse,youwillneed toobtainpermissiondirectly from thecopyrightholder.