Min-max control of uncertain multi-inventory systems with multiplicative uncertainties

In this note, we consider production-distribution systems with buffer and c apacity constraints. For such systems, we assume that the model is not know n exactly. More precisely, the entries of the matrix representing the syste m structure may be affine functions of some uncertain time-varying paramete rs that take values within assigned bounds. We give stabilizability conditi ons that can be checked, in principle, by solving a min-max problem an the surface of the state-space (buffer level space) unit ball. Then, we conside r a special Ease in which each uncertain parameter affects a single column of the system matrix and is independent of all the other ones. In this case , we propose a mixed integer linear programming algorithm to check the stab ilizability conditions and we provide a stabilizing control in an explicit form.