Analysis and Control of a Class of Stiff Linear Distributed Systems.
ILLINOIS UNIV AT URBANA DECISION AND CONTROL LAB
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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 clarifying their eigenvalue eigenvector pairs as epsilon approaches 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. Author
- Theoretical Mathematics