We present certainty equivalence output feedback results for discrete-time nonlinear systems that employ possibly discontinuous control laws in the feedback loop. Coupling assumptions of nominal robustness with uniform observability or delectability assumptions, we assert nominally robust stability for output feedback closed loops. We further show that model predictive control (MPC) can be used to generate a feedback control law that is robustly globally asymptotically stabilizing when used in a certainty equivalence output feedback closed loop. Allowing for discontinuous feedback control laws is important for systems employing MPC, since the method can, and sometimes necessarily does, result in discontinuous control laws. (c) 2004 Elsevier Ltd. All rights reserved.