Families of Liapunov Functions for Nonlinear Systems in Critical Cases

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dc.contributor.authorFu, Jyun-Horngen_US
dc.contributor.authorAbed, Eyad H.en_US
dc.contributor.departmentISRen_US
dc.date.accessioned2007-05-23T09:45:10Z
dc.date.available2007-05-23T09:45:10Z
dc.date.issued1990en_US
dc.description.abstractLiapunov functions are constructed for nonlinear systems of ordinary differential equations whose linearized system at an equilibrium point possesses either a simple zero eigenvalue or a complex conjugate pair of simple, pure emaginary eigenvalues. The construction is explicit, and yields parametrized families of Liapunov functions for such systems. In the case of a zero eigenvalue, the Liapunov functions contain quadratic and cubic terms in the state. Quadratic terms appear as well for the case of a pair of pure imaginary eigenvalues. Predictions of local asymptotic stability using these Liapunov functions are shown to coincide with those of pertinent bifurcation-theoretic calculations. The development of the paper is carried out using elementary properties of multilinear functions. The Liapunov function families thus obtained are amendable to symbolic computer coding.en_US
dc.format.extent1251112 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/4962
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; TR 1990-11en_US
dc.subjectIntelligent Servomechanismsen_US
dc.titleFamilies of Liapunov Functions for Nonlinear Systems in Critical Casesen_US
dc.typeTechnical Reporten_US

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