WIAS Preprint No. 561, (2000)

Hybrid method and vibrational stability for nonlinear singularly perturbed systems under parametric excitations


  • Strygin, Vadim V.

2010 Mathematics Subject Classification

  • 34E15


  • Hybrid asymptotical method, averaging, boundary functions, vibrational stability




The well-known classic feedback and feedforward techniques are the main tools for investigations of the control problems. Unlike these strategies, the vibrational control technique, introduced by S.M. Meerkov [1], has proven to be a viable alternative to conventional feedback and feedforward strategies in stabilization problems when the outputs, states and disturbances are difficult to access. Mathematical modelling of such systems is closely connected with nonlinear singularly perturbed systems under parametric excitations. In this paper a new asymptotical method based on the periodic solution theory, averaging method and boundary functions method, is presented. Due to it, a vibrational control problem can be investigated. The given example shows the "parasitic" parameters loss in such systems to be extremly dangerous.

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