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  • Letter
  • Open Access

Antiresonance in switched systems with only unstable modes

Maurizio Porfiri*

Russell Jeter

Igor Belykh†

  • Center for Urban Science and Progress, Department of Mechanical and Aerospace Engineering, and Department of Biomedical Engineering, New York University, Tandon School of Engineering, Brooklyn, New York 11201, USA

  • Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA

  • Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA and Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, 603950 Nizhny Novgorod, Russia

  • *Corresponding author: mporfiri@nyu.edu
  • †Corresponding author: ibelykh@gsu.edu
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Phys. Rev. Research 3, L022001 – Published 1 April, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L022001

Abstract

Antiresonance is a key property of dynamical systems that leads to the suppression of oscillations at select frequencies. We present the surprising example of a switched system that alternates between unstable modes, but exhibits antiresonance for a wide range of switching frequencies. We elucidate the stabilization mechanism and characterize the range of antiresonant frequencies for periodic and stochastic switching. The demonstration of antiresonance in a minimalistic variation of the Stuart-Landau model opens the door for a new paradigm in the study and design of switched systems.

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Phys. Rev. Research 3, L022001– Published 1 April, 2021
  • Received 9 October 2020
  • Revised 2 December 2020
  • Accepted 23 February 2021
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