Term of Award
Summer 2009
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Yan Wu
Committee Member 1
Xiezhang Li
Committee Member 2
Jimmy L. Solomon
Abstract
The Lorenz model is considered a benchmark system in chaotic dynamics in that it displays extraordinary sensitivity to initial conditions and the strange attractor phenomenon. Even though the system tends to amplify perturbations, it is indeed possible to convert a strange attractor to a non-chaotic one using various control schemes. In this work it is shown that the chaotic behavior of the Lorenz system can be suppressed through the use of a feedback loop driven by a quotient controller. The stability of the controlled Lorenz system is evaluated near its equilibrium points using Routh-Hurwitz testing, and the global stability of the controlled system is established using a geometric approach. It is shown that the controlled Lorenz system has only one globally stable equilibrium point for the set of parameter values under consideration.
Recommended Citation
Jones, Daniel C., "Stability Analysis of the Chaotic Lorenz System with a State-Feedback Controller" (2009). Electronic Theses and Dissertations. 944.
https://digitalcommons.georgiasouthern.edu/etd/944
Research Data and Supplementary Material
No
