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Families of Liapunov Functions for Nonlinear Systems in Critical Cases

dc.contributor.authorFu, Jyun-Horngen_US
dc.contributor.authorAbed, Eyad H.en_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 imaginary 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. Quartic 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-theorectic calculations. The development of the paper is carried out using elementary properties of multilinear functions. The Liapunov function families thus obtained are amenable to symbolic computer coding.en_US
dc.format.extent1407490 bytes
dc.relation.ispartofseriesISR; TR 1991-95en_US
dc.subjectnonlinear systemsen_US
dc.subjectspace structuresen_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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