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\begin{center} \Large Oral Qualifying Exam Syllabus \end{center}
\begin{center} Fernando Louro \end{center}
\begin{center} December 27, 2002 \end{center}
%{\center \Large Proposed PhD Oral Exam Syllabus for Fernando Louro}
\medskip

\begin{center}	\large Major Topic: Control Theory \end{center}

\begin{description}
\item Linear systems in discrete and continuous time. 
\item Minimum-norm control of time-varying linear systems.
\item Sufficient accessibility rank condition.
\item Feedback stabilization of LTI systems. Pole-shifting.
\item Unstable and stable modes.
\item Control-Lyapunov functions for LTI systems.
\item Realization theory for linear systems.
\item Observers and detectability. Dynamic feedback.
%\item[(7.4)] Frequency domain conrol, Nyquist criterion.
\item Continuous-time dynamic programming, Hamilton-Jacobi-Bellman equation.
\item Optimal control of LQ systems.
% linear systems with quadratic costs, Kalman
%	filtering, infinite time steady-state problems.
\item Optimal control using the Maximum Principle.
\end{description}
%{\small Section numbers above are from \cite{sontag}.}

\medskip

\begin{center}	\large Minor Topic: Asymptotics \end{center}
\begin{description}
\item Asymptotic series. Asymptotics of solutions of linear
	differential equations.
\item Asymptotic expansion of integrals: Watson's Lemma,
	Laplace's method, method of steepest descent,
	method of stationary phase.
\item Perturbation methods, asymptotic matching.
\item Boundary layer theory.
\item Elementary WKB theory.
\end{description}
%{\small Section numbers above are from~\cite{bender}. In particular,
%the minor topic syllabus covers all of~\cite{murray}.}

\nocite{sontag, bender, murray}
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