In this lecture we define the concept of stability. We link the concept of exponential stability to the existence of a positive solution to the Lyapunov equation. Furthermore, we show that the location of spectrum of the infinitesimal generator does not imply the stability of the associated semigroup. If the solution of the homogeneous abstract differential equation converses to zero, then the system is said to be strongly stable. The system (with an input) is stabilizable if there exists a feed