Model predictive control (MPC) has been widely adopted in the chemical and petrochemical industry due to its ability to account for actuator constraints and multi-variable interactions for complex processes. However, closed-loop stability is not guaranteed within the framework of MPC without additional constraints or assumptions. An MPC formulation that can guarantee closed-loop stability in the presence of uncertainty is Lyapunov-based model predictive control (LMPC) which incorporates stability constraints based on a stabilizing Lyapunov-based controller. Though LMPC drives the closed-loop state trajectory to a steady-state, it lacks the ability to adjust the rate at which the closed-loop state approaches the steady-state in an explicit manner. However, there may be circumstances in which it would be desirable, for safety reasons, to be able to adjust this rate to avoid triggering of safety alarms or process shut-down. In addition, there may be scenarios in which the current region of operation is no longer safe to operate within, and another region of operation (i.e., a region around another steady-state) is appropriate. Motivated by these considerations, this work develops two novel LMPC schemes that can drive the closed-loop state to a safety region (a level set within the stability region where process functional safety is ensured) at a prescribed rate or can drive the closed-loop state to a safe level set within the stability region of another steady-state. Recursive feasibility and closed-loop stability are established for a sufficiently small LMPC sampling period. A comparison between the proposed method, which effectively integrates feedback control and safety considerations, and the classical LMPC method is demonstrated with a chemical process example. The chemical process example demonstrates that the safety-LMPC drives the closed-loop state into a safe level set of the stability region two sampling times faster than under the classical LMPC in the presence of process uncertainty. (C) 2016 Elsevier Ltd. All rights reserved.