Abstract
In this paper we propose an optimization approach to compute low-complexity polyhedral invariant sets for discrete-time linear systems affected by delay, based on structural properties related to set factorization. A similarity transformation is conceived as a design tool to bring the dynamic matrix of an augmented representation of the delay difference equation to a block companion form for which low dimensional polyhedral invariant sets with fixed complexity can be found. An optimization problem is formulated to simultaneously compute the similarity transformation and the invariant polyhedron of pre-defined complexity. Numerical experiments illustrate the efficiency of the proposed approach.
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