This paper addresses the design of dynamic allocation functions for systems with saturating actuators. The allocator can redistribute the desired control effort within the multiple actuators by penalizing each actuator to be more or less used, while also taking into account a criterium for minimization of their total energy consumption over time. Anti-windup gains are added to both the controller and the dynamic allocator state to deal with the saturation condition. Convex conditions for the co-design of both the dynamic allocator and anti-windup gains are expressed in the form of linear matrix inequalities (LMIs). Such conditions allow to deal with the multiple objective problems of enlarging the estimates of the basin of attraction and minimizing the total energy consumption of the actuators. Two examples borrowed from the literature illustrate the proposed technique and show its effectiveness.