Economic model predictive control (EMPC) is a control scheme that combines real-time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time-varying process economics). In the present work, we focus on the development of a Lyapunov-based EMPC (LEMPC) scheme that is formulated with an explicitly time-varying economic cost function. First, the formulation of the proposed two-mode LEMPC is given. Second, closed-loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed-loop simulations of a chemical process that the proposed LEMPC can achieve stability with time-varying economic cost as well as improve economic performance of the process over a conventional MPC scheme. (c) 2013 American Institute of Chemical Engineers AIChE J 60: 507-519, 2014