TY - JOUR
T1 - Computation of Lyapunov–Perron transformation for linear quasi-periodic systems
AU - Subramanian, Susheelkumar C.
AU - Waswa, Peter M.B.
AU - Redkar, Sangram
N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Funding to support this research was partially provided by the Interplanetary Initiative of Arizona State University.
Publisher Copyright:
© The Author(s) 2021.
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - Lyapunov–Perron transformation
KW - nonlinear dynamics
KW - parametric excitation
KW - quasi-periodic system
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U2 - 10.1177/1077546321993568
DO - 10.1177/1077546321993568
M3 - Article
AN - SCOPUS:85100960977
SN - 1077-5463
VL - 28
SP - 1402
EP - 1417
JO - JVC/Journal of Vibration and Control
JF - JVC/Journal of Vibration and Control
IS - 11-12
ER -