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A Convex Approach for Stability Anal...

Arizona State University.

A Convex Approach for Stability Analysis of Partial Differential Equations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A Convex Approach for Stability Analysis of Partial Differential Equations.
作者:	Meyer, Evgeny.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2016
面頁冊數:	68 p.
附註:	Source: Masters Abstracts International, Volume: 55-05.
附註:	Adviser: Matthew Peet.
Contained By:	Masters Abstracts International55-05(E).
標題:	Mechanical engineering.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10133815
ISBN:	9781339923710

A Convex Approach for Stability Analysis of Partial Differential Equations.
Meyer, Evgeny.

A Convex Approach for Stability Analysis of Partial Differential Equations. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 68 p.

Source: Masters Abstracts International, Volume: 55-05.

Thesis (M.S.)--Arizona State University, 2016.

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.

ISBN: 9781339923710Subjects--Topical Terms:

190348
Mechanical engineering.

A Convex Approach for Stability Analysis of Partial Differential Equations.
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245 1 2 $a A Convex Approach for Stability Analysis of Partial Differential Equations.
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500 $a Source: Masters Abstracts International, Volume: 55-05.
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502 $a Thesis (M.S.)--Arizona State University, 2016.
520 $a 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.
520 $a 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&Dot;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 variables. An extra spatial variable allows consideration of problems such as local stability of fluid flows in channels and dynamics of population over two dimensional domains.
520 $a The approach does not involve discretization and is based on using Sum-of-Squares (SOS) polynomials and positive semi-definite matrices to parameterize operators which are positive on function spaces. Applying the parameterization to construct Lyapunov functionals with negative derivatives allows to express stability conditions as a set of LinearMatrix Inequalities (LMIs). The MATLAB package SOSTOOLS was used to construct the LMIs. The resultant LMIs then can be solved using existent Semi-Definite Programming (SDP) solvers such as SeDuMi or MOSEK. Moreover, the proposed approach allows to calculate bounds on the rate of decay of the solution norm.
520 $a The methodology is tested using several numerical examples and compared with the results obtained from simulation using standard methods of numerical discretization and analytic solutions.
590 $a School code: 0010.
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