Abstract
This paper deals with the computational issues encountered in the construction of invariant sets of uncertainty LTI systems, the presented results being useful in the more general framework of piecewise linear systems affected by parametric uncertainty. The main contribution is the efficient computation of upper and lower bounds of the maximal positively invariant (MPI) set. These turn to be meaningful approximations when iterative construction procedures are employed, especially if no finite-time algorithms exists to construct the exact MPI set. In order to decrease the computational complexity, the interval search procedures are used to avoid the treatment of the regions which do not meet the neighboring properties. Keywords: Model predictive control, Invariant sets, Dynamic uncertainties, Interval analysis.
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