Probabilistic reachable and invariant sets for linear systems with correlated disturbance

Paper on stochastic invariance; International audience; In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only bounds on the mean and the covariance matrices are supposed to be known. This allows to consider nonlinear stochastic systems approximations and the effect of nonlinear filters on the disturbance. The correlation bound concept is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given.