This paper deals with the characterization of all stabilizing \(\mathcal {H}_{\infty }\) controllers for plants described by any left coprime factors under an alternative framework, which is defined for both the continuous- and discrete-time cases. Moreover, we show that this framework can generate both continuous-time (strictly proper) and discrete-time (non-strictly proper) central controllers. In particular, the application will be carried out to track the trajectory of two-wheel non-holonomic mobile robots with differential drive used in robot soccer competitions in the Very Small Size (VSS) category. For simulation purposes, the structures of the discrete-time central controller and the continuous-time central controller applied to the same model of the robot under study will be presented. In addition, controller implementations will be presented, which will validate the effectiveness of the designed control systems against the references imposed on them.
