Theory of linear control systems -- Historical overview of automatic control -- Automatic control before the 1930's -- Classical period of automatic control -- Beginnings of modern control theory -- Modern control theory -- State-space representation -- System properties -- State feedback and optimal control -- State observers and estimators -- Solved problems -- Continuous linear systems -- Simple differential equations -- Matrix theory -- Systems of linear differential equations -- Input-output representation -- State-space representation -- Stability -- Controllability and observability -- Canonical realizations -- State feedback -- Optimal control -- State observers -- Kalman-Bucy filter -- Reduced-order observers -- Discrete linear systems -- Simple difference equations -- More matrix theory -- Systems of linear difference equations -- Input-output representation -- State-space representation -- Stability -- Controllability and observability -- Canonical realizations -- State feedback -- Optimal control -- State observers -- Kalman filter -- Reduced-order observers -- A quick introduction to MATLAB -- Basic matrix operations -- Plotting graphs -- Data analysis -- Data management and I/O operations -- Mathematical preliminaries -- Differential and difference equations -- Laplace and z-transforms -- Matrices and determinants -- Results from advanced matrix theory -- Eigenvectors and eigenvalues -- Diagonal and Jordan forms -- Similarity of matrices -- Symmetric and Hermitian matrices.