Date of Completion

Fall 1-6-2026

Thesis Advisor(s)

Chang Liu, Ali Gokirmak

Honors Major

Robotics Engineering

Disciplines

Acoustics, Dynamics, and Controls | Controls and Control Theory | Control Theory | Dynamical Systems | Dynamic Systems | Fluid Dynamics | Hydrology | Numerical Analysis and Scientific Computing | Oceanography | Ordinary Differential Equations and Applied Dynamics | Other Mechanical Engineering | Other Oceanography and Atmospheric Sciences and Meteorology

Abstract

This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the Lyapunov method is used to analyze the instantaneous principal direction of instability. The computational resources required by the Lyapunov method, numerical simulations, and Floquet theory are discussed..

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