Robust control of linear systems with bounded state dependent additive disturbances

This paper examines attractiveness and minimality of invariant sets for linear systems subject to additive disturbances bounded in a state-dependent set. Existence of a minimal attractor is proved under the assumption that the state-dependent set, to which the disturbance is confined, is upper-semi-continuous. In many practical applications, the disturbance may be an output of a dynamic process. The results for systems subject to general state dependent disturbances are applied to this case to prove existence of a minimal robust invariant attractor (MRIA). The MRIA set can be employed for the design of an MPC strategy to achieve the robust stability. Moreover, in case constraint sets are polytopes, a computational method is provided to approximate the MRIA.