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A Convex Approach for Stability Analysis of Partial Differential Equations


Abstract A computational framework based on convex optimization is presented for stability analysis of systems described by Partial Differential Equations (PDEs). Specifically, two forms of linear PDEs with spatially distributed polynomial coefficients are considered.

The first class includes linear coupled PDEs with one spatial variable. Parabolic, elliptic or hyperbolic PDEs with Dirichlet, Neumann, Robin or mixed boundary conditions can be reformulated in order to be used by the framework. As an example, the reformulation is presented for systems governed by Schr¨odinger equation, parabolic type, relativistic heat conduction PDE and acoustic wave equation, hyperbolic types. The second form of PDEs of interest are scalar-valued with two spatial ... (more)
Created Date 2016
Contributor Meyer, Evgeny (Author) / Peet, Matthew (Advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Arizona State University (Publisher)
Subject Mechanical engineering / Computer engineering / Aerospace engineering / Convex optimization / Lyapunov / PDEs / Stability
Type Masters Thesis
Extent 68 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Note Masters Thesis Mechanical Engineering 2016
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis