On stability of a harmonic oscillator with a delayed feedback system

Bachelor thesis (2019)

Authors

V.C.Y. Li Electrical Engineering, Mathematics and Computer Science

Contributors

W.T. van Horssen Mathematical Physics - EEMCS (mentor)
J.G. Spandaw Analysis - EEMCS (graduation committee member)
N.V. Budko Numerical Analysis - EEMCS (graduation committee member)
P. Verstraten Electrical Engineering, Mathematics and Computer Science (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2019 Vincent Li
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Published Date

03-07-2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this thesis the stability type of y=0 is being considered for the delay differential equation y''(t) + ay(t) + by(t-1) = 0 with a and b real numbers. It is already known that y=0 is stable when b=0 and a>0 and unstable when b=0 and a<0. The aim of this project is to determine the stability of y=0 for all values of a and b. First, the general stability theory for delay differential equations was highlighted before giving an in-depth stability analysis of the equation y''(t) + ay(t) + by(t-1) = 0. It turns out that a theorem of Pontryagin (1908 -1988) is really helpful for answering these stability questions. Due to this theorem all values for a and b are determined such that y=0 is asymptotically stable for y''(t) + ay(t) + by(t-1) = 0. However, this does not cover the stability type of y=0 for all values of a and b. So more analysis was done in order to give a full answer of the stability problem. The full answer was not achieved as there are still values for a and b where the stability is unknown. Finally, numerical solutions of y''(t) + ay(t) + by(t-1) = 0 are shown to confirm the results that are obtained.

Files

Thesis.pdf
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