Comparison of Poincare Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

Susheelkumar C. Subramanian, Sangram Redkar

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique and apply them towards the investigation of stability bounds for linear time periodic systems. Though the Normal Forms technique has been predominantly used for the analysis of nonlinear equations, in this work, the authors utilize it to transform a linear time periodic system to a time-invariant system, similar to the Lyapunov-Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation, and near identity transformations to facilitate the application of time-independent Normal Forms. This method provides a closed form analytical expression for the state transition matrix (STM). Additionally, stability analysis is performed on the transformed system and the comparative results of dynamical characteristics and temporal variations of a simple linear Mathieu equation are also presented in this work.

Original languageEnglish (US)
Article number014502
JournalJournal of Computational and Nonlinear Dynamics
Volume16
Issue number1
DOIs
StatePublished - Jan 2021
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

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