Robust stabilizing inventory control in supply networks under uncertainty of external demand and supply time-delays

A synthesis problem of the robust inventory control strategy for supply networks under uncertain bounded demand and uncertainty of supply time-delays and with presence of asymmetric constraints on states and controls is considered. Control is constructed based on the invariant ellipsoid method as a linear non-stationary feedback with respect to deviation of the current stock level from the chosen safety level. Solvability conditions of the synthesis problem are stated in the form of linear matrix inequalities and are reduced to solving semi-definite programming and one-dimensional convex optimization problems. The resulting control strategy ensures suppression of influence of intervalbounded external demand and robust stabilization of the closed-loop system. Control of the supply network of three nodes is considered as an example.