Classification on Boundary-Equilibria and Singular Continuums of Continuous Piecewise Linear Systems

Hebai Chen, Zhaosheng Feng, Hao Yang, Linfeng zhou
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Abstract

In this paper, we show that any switching hypersurface of [Formula: see text]-dimensional continuous piecewise linear systems is an [Formula: see text]-dimensional hyperplane. For two-dimensional continuous piecewise linear systems, we present local phase portraits and indices near the boundary equilibria (i.e. equilibria at the switching line) and singular continuum (i.e. continuum of nonisolated equilibria) between two parallel switching lines. The index of singular continuum is defined. Then we show that boundary-equilibria and singular continuums can appear with many parallel switching lines.
连续分段线性系统的边界平衡和奇异连续的分类
本文证明了[公式:见文]维连续分段线性系统的任意切换超平面是一个[公式:见文]维超平面。对于二维连续分段线性系统,我们给出了边界平衡点(即开关线上的平衡点)和两个平行开关线上的奇异连续统(即非孤立平衡的连续统)附近的局部相图和指标。定义了奇异连续统的指数。然后我们证明了边界平衡和奇异连续统可以在多个平行开关线下出现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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