The course provides students with a wide study in the state space representation and realization, in particular the controllability, the observability and the state space representation of linear systems are highlighted. Besides, many feedback control syntheses are addressed namely the pole placement control, the state observer based feedback control and the optimal control. The stability analysis is also carried out in the Lyapunov framework. Nevertheless, the digital control synthesis, the stability analysis in the Z-plane and the closed loop control paradigm are addressed in the last part of the course.