WIAS Preprint No. 624, (2000)

Geometric approach to vibrational control of singularly perturbed systems


  • Schneider, Klaus R.
  • Fridman, Emilia

2010 Mathematics Subject Classification

  • 34D05 34H05 93C15 93C70


  • vibrational, stabilization, singularly perturbed systems, normally hyperbolic invariant manifolds, averaging


We extend the theory of vibrational stabilizability to systems with fast and slow variables. The mathematical tools for establishing corresponding results are the persistence theory of normally hyperbolic invariant manifolds, the averaging theory and appropriate transformations. At the same time we introduce modified concepts of vibrational stabilizability compared with the 'classical' definitions.

Download Documents