This thesis focuses on developing a cognition-oriented robust controller to realize quadratic stabilization of unknown nonlinear systems. The core of the proposed control relies on a data-driven stability criterion, which is established according to the geometric interpretation of the quadratic Lyapunov stability condition. By properly arranging soft-computing techniques and the proposed stability criterion within a cognitive framework serving as basic cognitive functions and expert knowledge base, respectively, the proposed method can build the internal representation of the knowledge about the quadratic stability and the dynamics of the current motion of the system to be controlled. Based on these representations, suitable control input can be generated by the planning module of the proposed controller to stabilize the motion of the unknown systems. Due to these reasons, the propose controller can be classified into cognitive approaches. At the end of this thesis two numerical examples are shown to demonstrate the successful application and performance of the proposed control method.