Mathematical Models. 

1. 1. 1. 1. State space representations. 

         2. Linear models. 

         3. Nonlinear models and its linearization around equilibrium points and solutions.

Time domain analysis. 

1. 1. 1. 1. Output and state free response. 

         2. Natural modes and modal decomposition. 

         3. State and output forced response. 

         4. Impulsive and step response. 

         5. Rise time, settling time and maximal overshooting and undershooting.

Frequancy domain analysis. 

1. 1. 1. 1. Fundamental properties of Laplace transform and most used transforms. 

         2. Transfer functions. Input-output models.

Stability of linear systems. 

1. 1. 1. 1. Main notions and criteria. 

         2. Routh criterion.

Bode plots. 

1. 1. 1. 1. Armonic response. 

         2. Steady-state and transient response with sinusoidal and polynomial inputs.

Controllability and observability. 

1. 1. 1. 1. Controllability and observability grammians and matrices. 

         2. Hautus tests for controllability and observability. 

         3. Point-to-point control problems. State reconstruction problems.

Time domain design. 

1. 1. 1. 1. Eigenvalue assignment and state estimation and reconstruction. 

         2. Steady state performances.

Interconnected systems.

1. 1. 1. 1. Series, parallel and feedback interconnections. 

         2. General properties of feedback interconnections. 

         3. Zero-pole cancellations.

Stability of linear feedback systems. 

1. 1. 1. 1. Polar plots and Nyquist criterion. 

         2. Frequency domain design. 

         3. Proportional, derivative and integral control actions.

Root-locus. 

1. 1. 1. 1. Stabilization with root-locus methods.

         2. Pole assignment with root-locus methods.

Steady-state performance. 

Tracking and disturbance compensation. 

1. 1. 1. 1. Transient performances. 

         2. Open-loop phase margin and cross-over frequency versus closed-loop cut-off frequency and resonance peak.

         3.  Zero-pole control actions for phase margin and cross-over frequency modification.

         4. Introducing energy constraints on the controller