TY - GEN
T1 - Linear Stability of Plane Poiseuille Flow in the Sense of Lyapunov
AU - Edwards, Collin
AU - Peet, Yulia T.
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - In this paper, we present a linear stability analysis formulation for a plane Poiseuille flow developed in a continuous time domain. Contrary to a conventional approach based on an eigenvalue analysis, which can only proof stability with respect to certain solutions that are assumed to be time harmonics modulated by an exponentially growing or decaying amplitude, the presented methodology does not make any assumptions on a solution form. By analyzing all time-varying solutions and not only the ones restricted to a specific functional form, the developed stability test provides a stronger condition with regard to the system stability. Stability analysis is performed by first casting the corresponding linearized partial differential equation into a partial integral equation (PIE) form, and subsequently employing a linear partial inequality (LPI) stability test, which searches for a corresponding Lyapunov function parameterized through polynomial expansions to prove or disprove stability. Stability results of the continuous-time formulation for the plane Poiseuille flow are compared with a traditional eigenvalue-based analysis, demonstrating that the developed methodology represents a stricter condition on stability.
AB - In this paper, we present a linear stability analysis formulation for a plane Poiseuille flow developed in a continuous time domain. Contrary to a conventional approach based on an eigenvalue analysis, which can only proof stability with respect to certain solutions that are assumed to be time harmonics modulated by an exponentially growing or decaying amplitude, the presented methodology does not make any assumptions on a solution form. By analyzing all time-varying solutions and not only the ones restricted to a specific functional form, the developed stability test provides a stronger condition with regard to the system stability. Stability analysis is performed by first casting the corresponding linearized partial differential equation into a partial integral equation (PIE) form, and subsequently employing a linear partial inequality (LPI) stability test, which searches for a corresponding Lyapunov function parameterized through polynomial expansions to prove or disprove stability. Stability results of the continuous-time formulation for the plane Poiseuille flow are compared with a traditional eigenvalue-based analysis, demonstrating that the developed methodology represents a stricter condition on stability.
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U2 - 10.1109/CDC49753.2023.10383471
DO - 10.1109/CDC49753.2023.10383471
M3 - Conference contribution
AN - SCOPUS:85184821450
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4693
EP - 4698
BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 62nd IEEE Conference on Decision and Control, CDC 2023
Y2 - 13 December 2023 through 15 December 2023
ER -