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On the computation and bounding of invariant sets

This contribution deals with the computational issues encountered in the construction of invariant sets, the presented results being useful in the more general framework of piecewise linear systems. The main contribution of the present paper is the efficient computation of upper and lower bounds of the maximal positive invariant (MPI) sets. 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, interval search procedures are used to avoid the treatment of the regions which do not meet the neighboring properties.