Linear Systems Theory

Review of elementary linear algebra. Eigenspaces. Vector space partitions. Vector matrix differential equations. The transition matrix. State space theory of linear dynamical systems. Reachability and pole assign ability. Introduction to optimal control with quadratic cost. The Lyapunov matrix equation and the matrix Ricatti equation. Introduction to polynomial algebras leading to system theory in the Frequency domain. The system matrix. Introduction to Lyapunov stability theory. Random processes in dynamical systems. Use of MATLAB, Simulink and Control Toolbox software.