A control strategy proposed by the authors in previous works to reduce the effect of chattering led to the solution of a differential inequality involving the first and second derivatives of the control signal and a parameter for a first-order observer, The analysis was carried out assuming this parameter to be constant, In the present paper, this assumption is removed, thus allowing the solution of the differential inequality to be a function of a piecewise continuous first derivative of the control signal, without need for assuming a priori knowledge of bounds to the plant trajectories.