In this work, we consider moving horizon state estimation (MHE)-based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov-based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670-1680; Syst Control Lett. 2006;55:650-659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376-386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed-loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE-based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed-loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open-loop operation. A chemical process is used to illustrate the proposed approaches. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 4273-4286, 2013