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In this paper a constructive method to determine and compute probabilisticreachable and invariant sets for linear discrete-time systems, excited by astochastic disturbance, is presented. The samples of the disturbance signal arenot assumed to be uncorrelated, only a bound on the correlation matrices issupposed to be known. The concept of correlation bound is introduced andemployed to determine probabilistic reachable sets and probabilistic invariantsets. Constructive methods for their computation, based on convex optimization,are given.

Probabilistic reachable and invariant sets for linear systems with correlated disturbance