This paper addresses the performance recovery of explicit model predictive control (eMPC) when states of the system are not available via measurement. It is shown that the performance of the closed-loop system under the eMPC controller can be degraded when using a state observer instead of measurement. To moderate this degradation, an optimization-based approach is proposed that enables the designer to systematically design an optimal observer. It is proved that the proposed approach leads to the maximum achievable performance (in some sense) when compared to the desired performance (i.e. when states are available via measurement). Simulation results illustrate the performance and effectiveness of the proposed approach compared to a set of observers designed using a robust pole-placement approach.
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