This paper proposes a new approach to the Pulse Width Modulation strategies of multilevel Voltage Source Inverters. In this study, the modelling is focused on a flying capacitor three-level topology. This mathematical approach is based on the concepts of pseudo inverse and generalized inverse. The study allows recovering classical Pulse Width Modulation (PWM) solutions. It also offers a new investigative tool to explore the degree of freedom provided by the duty cycle solution set.