Computation of Lyapunov–Perron transformation for linear quasi-periodic systems

Susheelkumar C. Subramanian, Peter M.B. Waswa, Sangram Redkar

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The transformation of a linear time periodic system to a time-invariant system is achieved using the Floquet theory. In this work, the authors attempt to extend the same toward the quasi-periodic systems, using a Lyapunov–Perron transformation. Though a technique to obtain the closed-form expression for the Lyapunov–Perron transformation matrix is missing in the literature, the application of unification of multiple theories would aid in identifying such a transformation. In this work, the authors demonstrate a methodology to obtain the closed-form expression for the Lyapunov–Perron transformation analytically for the case of a commutative quasi-periodic system. In addition, for the case of a noncommutative quasi-periodic system, an intuitive state augmentation and normal form techniques are used to reduce the system to a time-invariant form and obtain Lyapunov–Perron transformation. The results are compared with the numerical techniques for validation.

Original languageEnglish (US)
JournalJVC/Journal of Vibration and Control
DOIs
StateAccepted/In press - 2021
Externally publishedYes

Keywords

  • Lyapunov–Perron transformation
  • nonlinear dynamics
  • parametric excitation
  • quasi-periodic system

ASJC Scopus subject areas

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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