Course Content (Syllabus)
1. Modeling (state-space, modeling of dynamical systems in the state-space, mathematical modeling, mathematical modeling examples).
2. Fundamental Properties of Dynamical Systems (dynamical system solution, equilibrium points, limit cycles, stability definitions, stability of linear systems, stability analysis via linear approximation, Lyapunov stability analysis, Lasalle’s Invariance Theorem).
3. Linear Systems (linearity, time-invariance, initial state response, the transition matrix and its derivation, eigenvalues and rhythms, input-output response, linearization).
4. Linear State Feedback Control (controllability (definition, criteria), uncontrollable form, stabilization, controllable canonical form, stabilization via state feedback, eigenvalue assignment, state feedback control design, linear quadratic regulator).
5. Linear Output Feedback Control (Observability (definition, criteria), observable canonical form, state estimation-observers, control with observers, Kalman’s decomposition).
6. Control Design in the Presence of Uncertainties (robust performance, modeling errors, disturbance rejection, Lyapunov re-design, robust linear control design).