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

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.