A necessary and sufficient condition for stability of a class of planar nonlinear systems

Yunlei Zou,Chunjiang Qian,Shuaipeng He

doi:10.1016/j.automatica.2020.109198

Yunlei Zou, Chunjiang Qian + Show 1 more

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https://doi.org/10.1016/j.automatica.2020.109198

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Journal: Automatica	Publication Date: Aug 18, 2020
Citations: 4	License type: publisher-specific-oa

Affiliation: The University of Texas at San Antonio, Yangzhou University

Abstract

In this paper, the stability problem of a class of planar nonlinear systems is investigated. Motivated by the Routh–Hurwitz stability criterion for planar linear systems, a necessary and sufficient condition for stability of a class of planar nonlinear systems is established. To prove the necessity, a new method called particular solution method is provided to justify instability. In addition, a sufficient condition for existence of oscillations is introduced. The necessary and sufficient condition can provide a simple way to design controllers by adjusting control parameters for some planar nonlinear systems.

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