**Abstract**

The present chapter focuses on some recent work on the qualitatively analysis of dynamical systems, namely stability, a powerful tool with multiple connected appliances. Among them, feedback is a powerful idea which is used extensively in natural and technological systems. In engineering, feedback has been rediscovered and patented many times in many different contexts. Stabilizing a dynamical system could be often easier if we approach *controllable systems*. When the dynamical system is in a controllable form, we can place bounds on its behavior by analyzing the improvement of the linear and nonlinear operators that describe the system. In this chapter it is analyzed how a control in a simple form, could influence the possibility to construct the so-called *Control Lyapunov Function (CLF)* in order to stabilize the dynamical system in study. The main idea is to test multiple cases, in order to get a rich information panel and to make easier the problem of finding a CLF, which is generally a difficult task. As applications, models from excitable media are chosen.

**Keywords:** dynamical systems in control, Lyapunov stabilities, stabilization by feedback, Lyapunov and storage function, feedback control, computational methods, algebraic methods
