2026-09-25T11:51:48Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/97932021-07-05T14:03:20Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Jean-Jacques E. Slotine.
Lohmiller, Winfried Stefan, 1971-
Massachusetts Institute of Technology. Department of Mechanical Engineering
2005-08-19T20:13:05Z
2005-08-19T20:13:05Z
1999
1999
http://hdl.handle.net/1721.1/9793
42916380
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.
Includes bibliographical references (leaves 87-90).
This thesis derives new results in nonlinear system analysis using methods inspired from fluid mechanics and differential geometry. Based on a differential analysis of convergence, these results may be viewed as generalizing the classical Krasovskii theorem, as well as linear eigenvalue analysis. A central feature is that convergence and limit behavior are in a sense treated separately, leading to significant conceptual simplifications. We establish new combination properties of nonlinear dynamic systems and use them to derive simple controller and observer designs for mechanical systems such as aircraft, underwater vehicles, and robots. The method is also applied to chemical chain reactions and mixture processes. The relative simplicity of these designs stems from their effective exploitation of the systems' structural specificities. Next, we analyze and quantify the global stability properties of physical partial differential equations such as the heat equation, or the Schroedinger equation. Lyapunov exponents are not coordinate-invariant, and thus their exact physical meaning is somewhat questionable. As an alternative, we suggest an extension of linear eigenvalue analysis to nonlinear dynamic systems. Finally, the thesis derives new controller and observer designs for general nonlinear dynamic systems. In particular, an extension of feedback linearization is proposed when the corresponding integrability conditions are violated.
by Winfried Stefan Lohmiller.
Ph.D.
90 leaves
5848748 bytes
5848504 bytes
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eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mechanical Engineering
Contraction analysis of nonlinear systems
Thesis
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