Stability and Robustness Analysis of Quasi-Periodic System Subjected to Uncertain Parametric Excitations and Nonlinear Perturbations

Susheelkumar C. Subramanian, Sangram Redkar

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov–Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante’s approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this study, the same approach is extended toward linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov’s direct approach is employed to formulate the stability conditions a for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability can be derived for such systems. The applications of stability theorems are demonstrated with practical examples of commutative and noncommutative quasi-periodic systems.

Original languageEnglish (US)
Article number051010
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume144
Issue number5
DOIs
StatePublished - Oct 2022

Keywords

  • dynamics
  • nonlinear vibration
  • random vibration
  • stability

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

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