Analysis and Control of a Class of Stiff Linear Distributed Systems

This thesis examines a class of systems whose models are described by linear partial differential equations that depend on a small parameter (epsilon). First, the spectral decomposition of the so-called "stiff" operators (using the terminology of {24}) is investigated, including the convergence of their eigenvalue-eigenvector pairs as (epsilon) (--->) 0, with the objective of clarifying their singular behavior. Second, asymptotic approximation of the solution boundary value problems involving stiff operators are constructed, using the weak limits of their eigenvectors. This approach leads to a decomposition into "regular" approximation and "internal layer" approximation, which are found separately and then combined to provide an approximation to the original problem. This methodology is not complicated. Moreover, it alleviates the inherent stiffness when numerical algorithms are employed. Third, the same approach is applied to some control problems. In this case, similar results are obtained, provided additional requirements are satisfied, due to the type of control, which may drastically alter the system behavior.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Salhi, Hassen

• Engineering, Electronics and Electrical

Identifier

(UMI)AAI8324634

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69258