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arXiv · 1808.02253

Analysis of intersections of trajectories of linear systems

Amey Deshpande·Varsha Daftardar-Gejji·Palaniappan Vellaisamy
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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.

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Amey Deshpande, Varsha Daftardar-Gejji, Palaniappan Vellaisamy. 2018-08-07. Analysis of intersections of trajectories of linear systems. https://arxiv.org/abs/1808.02253

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