  The control of constrained systems using model predictive control (MPC)
becomes more challenging when full state information is not available and when
the nominal system model and measurements are corrupted by noise. Since these
conditions are often seen in practical scenarios, techniques such as robust
output feedback MPC have been developed to address them. However, existing
approaches to robust output feedback MPC are challenged by increased complexity
of the online optimization problem, increased computational requirements for
controller synthesis, or both. In this work we present a simple and efficient
methodology for synthesizing a tube-based robust output feedback MPC scheme for
linear, discrete, time-invariant systems subject to bounded, additive
disturbances. Specifically, we first formulate a scheme where the online MPC
optimization problem has the same complexity as in the nominal full state
feedback MPC by using a single tube with constant cross-section. This makes our
proposed approach simpler to implement and less computationally demanding than
previous methods for both online implementation and offline controller
synthesis. Secondly, we propose a novel and simple procedure for the
computation of robust positively invariant (RPI) sets that are approximations
of the minimal RPI set, which can be used to define the tube in the proposed
control scheme.
