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Oscillations in First-Order, Continuous-Time Systems via Time-Delay Feedback

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  • Abimael Salcedo
  • Joaquin Alvarez

Abstract

A technique to generate (periodic or nonperiodic) oscillations systematically in first-order, continuous-time systems via a nonlinear function of the state, delayed by a certain time , is proposed. This technique consists in choosing a nonlinear function of the delayed state with some passivity properties, tuning a gain to ensure that all the equilibrium points of the closed-loop system be unstable, and then imposing conditions on the closed-loop system to be semipassive. We include several typical examples to illustrate the effectiveness of the proposed technique, with which we can generate a great variety of chaotic attractors. We also include a physical example built with a simple electronic circuit that, after applying the proposed technique, displays a similar behavior to the logistic map.

Suggested Citation

  • Abimael Salcedo & Joaquin Alvarez, 2018. "Oscillations in First-Order, Continuous-Time Systems via Time-Delay Feedback," Complexity, Hindawi, vol. 2018, pages 1-14, October.
    • Handle: RePEc:hin:complx:2178031
    DOI: 10.1155/2018/2178031
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