In this paper we consider an $ n $ dimensional piecewise smooth dynamical system. This system has a co-dimension 2 switching manifold $ \Sigma $ which is an intersection of two hyperplanes $ \Sigma_1 $ and $ \Sigma_2 $. We investigate the relation between periodic orbit of PWS system and periodic orbit of its double regularized system. If this PWS system has an asymptotically stable sliding periodic orbit(including type Ⅰ and type Ⅱ), we establish conditions to ensure that also a double regularization of the given system has a unique, asymptotically stable, periodic orbit in a neighbourhood of $ \gamma $, converging to $ \gamma $ as both of the two regularization parameters go to $ 0 $ by applying implicit function theorem and geometric singular perturbation theory.
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Sliding periodic orbit of type Ⅰ
Sliding periodic orbit of type Ⅱ