Analysis of intersections of trajectories of linear systems
Abstract
Present article deals with trajectorial intersections in linear fractional systems ('systems'). We propose a classification of intersections of trajectories in three classes viz. trajectories intersecting at same time(EIST), trajectories intersecting at distinct times(EIDT) and self intersections of a trajectory. We prove a generalization of separation theorem for the case of linear fractional systems. This result proves existence of EIST. Based on the presence of EIST, systems are further classified in two types; Type I and Type II systems, which are analyzed further for EIDT. Besides constant solutions and limit-cycle behavior, a fractional trajectory can have nodal or cuspoidal intersections with itself. We give a necessary and sufficient condition for a trajectory to have such types of intersections.
Keywords
Cite
@article{arxiv.1808.02253,
title = {Analysis of intersections of trajectories of linear systems},
author = {Amey Deshpande and Varsha Daftardar-Gejji and Palaniappan Vellaisamy},
journal= {arXiv preprint arXiv:1808.02253},
year = {2018}
}
Comments
16 pages, 4 figures