SummaryIn this paper, we propose the novel concept of “control storage function” and introduce upper and lower bounds to the best asymptotic average performance for nonlinear control systems based on suitable notions of dissipativity and controlled dissipativity. This allows to extend and unify the formulation and analysis of economic model predictive control for general optimal operation regimes, including, in particular, steady‐state or periodic operation. A closed‐loop economic performance and stability analysis are carried out within this generalized framework. As a special case, when the optimal operation is periodic, we present a new approach to formulate terminal cost functions. Finally, several examples and counterexamples are proposed and discussed to show the merits of the proposed approach.