TY - GEN
T1 - Lyapunov Perron Transformation for Linear Quasi-Periodic Systems
AU - Subramanian, Susheelkumar C.
AU - Redkar, Sangram
AU - Waswa, Peter
N1 - Publisher Copyright:
Copyright © 2020 ASME.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Lyapunov perron transformation
KW - Nonlinear dynamics
KW - Quasi periodic system
UR - http://www.scopus.com/inward/record.url?scp=85096345148&partnerID=8YFLogxK
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U2 - 10.1115/DETC2020-22230
DO - 10.1115/DETC2020-22230
M3 - Conference contribution
AN - SCOPUS:85096345148
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020
Y2 - 17 August 2020 through 19 August 2020
ER -