Robust invariant sets for constrained storage systems

Several items are produced and stored into nn buffers in order to supply an external demand without interruptions. We consider the classical problem of determining control laws and smallest buffer levels guaranteeing that an unknown bounded demand is always satisfied. A simple model with nn decoupled integrators and nn additive bounded disturbances is employed. The coupling arises from bounds on the total production capacity and on the total demand. Invariant set theory for linear and switched linear systems is exploited to compute robust positive invariant sets and controlled robust invariant sets for two commonly adopted scheduling policies. This paper provides the explicit expression of the invariant sets for any arbitrary nn.