WIAS Preprint No. 246, (1996)

On the asymptotic analysis of singularly perturbed systems with sliding mode


  • Fridman, Leonid M.
  • Rumpel, Rainer J.

2010 Mathematics Subject Classification

  • 34C15 34E10


  • sliding mode, discontinuous, singularly perturbed, nonlinear oscillations, dry friction, relay control




In this paper we study singularly perturbed systems with discontinuity surfaces. This means that we have a system of ordinary differential equations with a small parameter and a piecewise smooth vector field. The state where the trajectory moves on the discontinuity surface is called sliding mode. We present an asymptotic representation for trajectories with temporary sliding and apply the result to stick-slip vibrations.

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