Description: This article deal with the problem of obtaining delay-dependent stability conditions for a class of discrete-time supply networks with uncertain supply time-delays under unknown, but bounded external demand. An approach to solve the estimation problem of the maximum allowable upper bound of delay when synthesizing the inventory control system is proposed. Descriptor transformation of discrete model in states space of supply network node is applied. The Lyapunov-Krasovskii functional which depends on delay interval size for descriptor model is constructed. Construction of Lyapunov-Krasovskii functional is executed on the basis of decomposition the delay interval into two unequal subintervals. This leads to reduction of conservatism in terms of the upper bounds of the maximum time-delay. The computational algorithm for the choice of the tuning parameter defining a point of splitting the delay interval is offered. The sufficient condition of existence of the guaranteed controller which minimizes the upper boundary value of quadratic quality criterion is received. The considered problem is reduced to a semidefinite programming problem by means of linear matrix inequalities technique. A numerical example is provided.
Keywords: inventory control, guaranteed cost control, invariant ellipsoids method, Lyapunov-Krasovskii functional, linear matrix inequality, semidefinite programming