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arXiv · 1712.07356

Bifurcation of limit cycles from a switched equilibrium in planar switched systems and its application to power converters

Oleg Makarenkov
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Abstract

We consider a switched system of two subsystems that are activated as the trajectory enters the regions $\{(x,y):x>\bar x\}$ and $\{(x,y):x<-\bar x\}$ respectively, where $\bar x$ is a positive parameter. We prove that a regular asymptotically stable equilibrium of the associated Filippov equation of sliding motion (corresponding to $\bar x=0$) yields an orbitally stable limit cycle for all $\bar x>0$ sufficiently small. The research is motivated by an application to a dc-dc power converter, where $\bar x>0$ is used in place of $\bar x=0$ to avoid sliding motions.

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Oleg Makarenkov. 2017-12-20. Bifurcation of limit cycles from a switched equilibrium in planar switched systems and its application to power converters. https://arxiv.org/abs/1712.07356

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