Robust control in uncertain multi-inventory systems and consensus problems

We consider a continuous time linear multi-inventory system with unknown demands bounded within ellipsoids and controls bounded within polytopes. We address the problem of epsilon-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which epsilon-stabilizability is possible through a saturated linear state feedback control. The idea of this approach is similar to the consensus problem solution for a network of continuous time dynamic agents, where each agent evolves according to a first order dynamics has bounded control and it is subject to unknown but bounded disturbances. In this context, we derive conditions under which consensus can be reached. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.