Robust invariant set theory applied to networked buffer-level control

A manufacturer producing several items keeps them into safety stocks (buffers) in order to supply an external stochastic demand without interruptions. We consider the classical problem of determining stock levels guaranteeing that a stochastic bounded demand is always satisfied. A simple n-th integrator model with additive disturbances is employed. Invariant set theory for linear and switched linear systems is used to compute robust positive invariant sets and controlled robust invariant sets for two commonly used scheduling policies. This paper provides the explicit expression of the invariant sets for any arbitrary n.