In this paper, a novel approach is presented to design an optimal robust observer for polytopic systems using the direct searching method and the concept of inverse systems. First, a Luenberger observer is considered for a sample polytopic system. By applying the direct searching algorithm, the sub-regions of the observer design space that can make the estimation error dynamics asymptotically stable is determined. Then, by applying the Bounded Real Lemma for the inverse system of estimation error dynamics, the optimal gain of the observer is found. The simulation results are presented to prove the effectiveness of the proposed algorithm. The proposed approach is applied to a simulated model of a tramway system and the results are satisfactory.
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