Stability of the damped Mathieu equation with time delay

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Abstract

In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as ẍ (t) + KẊ (t) + (δ + ε cost) × (t) = bx (t - 2π). This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts describe the intriguing stability properties of an important class of delayed oscillatory systems subjected to parametric excitation.

Original languageEnglish
Pages (from-to)166-171
Number of pages6
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Volume125
Issue number2
DOIs
Publication statusPublished - Sep 26 2003

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Keywords

  • Parametric excitation
  • Stability
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications

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