Piecewise affine systems have emerged as focal points of study within the realm of control theory due to their ability to accurately model complex, non-linear dynamical systems. This thesis navigates the motivations behind the extensive investigation of piecewise affine systems and elucidates their practical utility. The inherent flexibility of piecewise affine models allows for a perfect representation of systems that exhibit distinct behaviors in different regions. This attribute makes them particularly well suited for applications in robotics, power systems, and process control, where the ability to capture nonlinearity is crucial. Examining the convenience of piecewise affine systems in control scenarios reveals their capacity to address challenging dynamics and facilitate the design of efficient control strategies.