2019年1月19日
A characterization of Filippov vector fields
- 記述言語
- 掲載種別
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Filippov's method is widely used in the literature to define vector fields on<br />
a discontinuity set of piecewise-continuous vector fields. However, it is not<br />
the only definition that has been proposed, and its theoretical assumptions are<br />
not well understood. The aim of this paper is to characterize Filippov's method<br />
such that its appropriateness can be examined. First, we provide a general<br />
formulation of sliding vector fields, and then characterize the Filippov vector<br />
field in terms of geometric and dynamical conditions via elementary methods.<br />
Our results show that the Filippov vector field follows from reasonable<br />
requirements as a generalization of continuous vector fields.
a discontinuity set of piecewise-continuous vector fields. However, it is not<br />
the only definition that has been proposed, and its theoretical assumptions are<br />
not well understood. The aim of this paper is to characterize Filippov's method<br />
such that its appropriateness can be examined. First, we provide a general<br />
formulation of sliding vector fields, and then characterize the Filippov vector<br />
field in terms of geometric and dynamical conditions via elementary methods.<br />
Our results show that the Filippov vector field follows from reasonable<br />
requirements as a generalization of continuous vector fields.
- ID情報
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- arXiv ID : arXiv:1901.06333