This paper deals with sufficient conditions for the asymptotical stability of a mass flow controlled system. Because of the presence of a saturation an anti-windup control structure is considered to manage saturation effects. In order to analyse the stability and the dynamic performance of the controlled system a Lyapunov approach is proposed. Through this approach, conditions on the three parameters which characterise the controller (PI and anti-windup controller) are found which guarantee the asymptotical stability of the controlled system.