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Explicit periodic solutions in a model of a relay controller with delay and forcing

Research output: Working paperWorking paper and Preprints

Original languageEnglish
StateUnpublished - 2004


In this paper we use a combination of numerical and analytical methods to find and construct solutions of a cameo model of relay control, formulated as a piecewise-constant delay differential equation (DDE). Numerical solutions of a related equation, where the discontinuities of the original DDE are smoothed out, are used to guide the construction of explicit solutions of the original DDE. On the other hand, the construction of explicit solutions provides starting data for numerical continuation of the smoothed equation. The stability of the explicit solutions can also be inferred from the numerical approach.

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  • 2004r25

    Submitted manuscript, 455 KB, PDF-document


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