Lyapunov Perron Transformation for Linear Quasi-Periodic Systems

Susheelkumar C. Subramanian, Sangram Redkar, Peter Waswa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

It is known that a Lyapunov Perron (L-P) transformation converts a quasi-periodic system into a reduced system with a time-invariant coefficient. Though a closed form expression for L-P transformation matrix is missing in the literature, the application of combination of multiple theories would aid in such transformation. In this work, the authors have worked on extending the Floquet theory to find L-P transformation. As an example, a commutative system with linear quasi-periodic coefficients is transformed into a system with time-invariant coefficient analytically. Furthermore, for non-commutative systems, similar results are obtained in this work, with the help of an intuitive state augmentation and Normal Forms technique. The results of the reduced system are compared with the numerical integration technique for validation.

Original languageEnglish (US)
Title of host publication16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791883914
DOIs
StatePublished - 2020
Externally publishedYes
EventASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 - Virtual, Online
Duration: Aug 17 2020Aug 19 2020

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume2

Conference

ConferenceASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020
CityVirtual, Online
Period8/17/208/19/20

Keywords

  • Lyapunov perron transformation
  • Nonlinear dynamics
  • Quasi periodic system

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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