In this thesis, we focused on two main themes of control theory, namely the study of delay systems and observation of impulsive systems. In the first part, we treated the problem of absolute stability and stabilization of Lur'e systems with variable delay in range. The criteria are provided in the form of linear matrix inequalities(LMI). Then we studied the exponential stability of a practical class of non autonomous nonlinear systems with delay, whose origin is not a point of equilibrium. In the second part, we began the problem of practical stabilization of uniform exponential nonlinear systems with multiple delays via linear control. Finally, we built observers for linear and nonlinear impulsive systems, inspired by those already established in the continuous case. A separation principle is also established.
