Families of Liapunov Functions for Nonlinear Systems in Critical Cases
| dc.contributor.author | Fu, Jyun-Horng | en_US |
| dc.contributor.author | Abed, Eyad H. | en_US |
| dc.contributor.department | ISR | en_US |
| dc.date.accessioned | 2007-05-23T09:48:51Z | |
| dc.date.available | 2007-05-23T09:48:51Z | |
| dc.date.issued | 1991 | en_US |
| dc.description.abstract | Liapunov 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.extent | 1407490 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/5141 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | ISR; TR 1991-95 | en_US |
| dc.subject | aircraft | en_US |
| dc.subject | nonlinear systems | en_US |
| dc.subject | space structures | en_US |
| dc.subject | stability | en_US |
| dc.subject | Intelligent Servomechanisms | en_US |
| dc.title | Families of Liapunov Functions for Nonlinear Systems in Critical Cases | en_US |
| dc.type | Technical Report | en_US |
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