Robust control of uncertain multi-inventory systems

We consider a continuous time linear multi-inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or 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. 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. Numerical simulations are provided.