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Computation of Polyhedral Positive Invariant Sets via Linear Matrix Inequalities

This paper presents a linear matrix inequality based algorithm for computation of polyhedral positive invari- ant sets for linear discrete-time systems subject to bounded state and input constraints. While the main algorithm is suitable for computation of polyhedral invariant sets of a general shape, a second algorithm specialized for symmetric sets is also presented. The results are extended to include polytopic uncertainty. Verification and demonstration of the proposed scheme is done through numerical examples.