In this paper, we first introduce upper and a lower bounds of the best asymptotic average performance for nonlinear control systems based on the concepts of dissipativity and control storage functions. This allows to extend the formulation and analysis of Economic Model Predictive Control to more general optimal operation regimes, such as periodic solutions. A performance and stability analysis is carried out within this generalized framework. Finally two examples are proposed and discussed to show the merits of the proposed approach.