Robust Positively Invariant Sets for Linear Systems subject to model-uncertainty and disturbances

In this paper, we propose an algorithm for the computation of Robust Positively Invariant sets for linear discrete-time systems subject to norm-bounded model-uncertainty, additive disturbances and polytopic constraints on the input and state. The invariant set (optimized with respect to a measure of size) and the corresponding controller are computed simultaneously by solving a single LMI optimization problem. The novelty lies in the fact that the proposed scheme explicitly takes account of (norm-bounded) model-uncertainty and does not require any iterative computations or initial estimates of the invariant set or controller. A numerical example, taken from literature, demonstrates the applicability of proposed algorithm.