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Abstract The problem of robust guaranteed inventory control synthesis for supply networks with parametric uncertainty under action of unknown, but bounded external demand and availability of non-symmetrical constraints on the values of states and controls is solved. The control law is constructed in the form of a linear dynamic feedback with respect to deviation between cash and safety stock levels of resources. In order to suppress the influence of external perturbations, modeling changes in demand, while ensuring robust stability of the closed system the method of invariant ellipsoids is used, which has been improved through the use descriptor system approach and building parameter-dependent Lyapunov function, which reduces the impact degree of uncertainty of the transport time-delays on the result of the synthesis control. With the help of the linear matrix inequalities technique the control synthesis problem is presented as a series of semidefinite programming, for solving which is used open source software. In the framework of the proposed method is possible to choose the optimal values of safety stock levels of resources, as the resulting solution determines, in fact, an algorithmic relationship between the levels of safety stocks and the optimal value of the quality criterion. The numerical example is considered. References Щербаков П. С. Приближенные методы в параметрической робастности линей-ных систем управления : дис. ... д-ра физ.-мат. наук : 05.13.01 / Щербаков Павел Сергеевич. – М. : , 2004. – 215 с. 2. Blanchini F. Feedback control of production-distribution systems with unknown demand and delays / F. Blanchini, R. Pesenti, F. Rinaldi, W. Ukovich // IEEE Transactions on Robotics and Automation. – 2000. – Vol. 16, No. 3. – P. 313–317. 3. Дорофеев Ю. И. Построение математических моделей управляемых сетей поставок с учетом запаздываний потоков / Ю. И. Дорофеев, А. А. Никульченко // Системні дослідження та інформаційні технології. – 2013. – № 1. – С. 16–27. 4. Лотоцкий В. А. Модели и методы управления запасами / В. А. Лотоцкий, А. С. Мандель. – М. : Наука, 1991. – 188 c. 5. Поляк Б. Т. Управление линейными системами при внешних возмущениях: техника линейных матричных неравенств / Б. Т. Поляк, М. В. Хлебников, П. С. Щербаков. – М. : ЛЕНАНД, 2014. – 560 с. 6. Blanchini R. Set-theoretic methods in control / R. Blanchini, S. Miani. – Boston: Birkh user, 2008. – 494 p. 7. Чурилов А. Н. Исследование линейных матричных неравенств. Путеводитель по программным пакетам / А. Н. Чурилов, A. B. Гессен. – СПб: С.-Петерб. гос. ун-т, 2004. – 148 с. 8. Feron E. Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions / E. Feron, P. Apkarian, P. Gahinet // IEEE Transactions on Automatic Control. – 1996. – Vol. 41. – P. 1041–1046. 9. Oliveira M. C. A new discrete-time robust stability condition / М. C. Oliveira, J. Bernussou, J. C. Geromel // System & Control Letters. – 1999. – Vol. 37. – P. 261–265. 10. Zhang W. Robust stability test for uncertain discrete-time systems: a descriptor system approach / W. Zhang, H. Su, Y. Liang, Z. Han // Latin American Applied Research. – 2011. – Vol. 41, No. 4. – P. 359–364. 11. Дорофеев Ю. И. Синтез системы оптимального управления запасами с дискретным ПИД-регулятором с использованием ЛМН / Ю. И. Дорофеев // Збірник наукових праць Харківського університету Повітряних Сил. – Х. : ХУПС, 2014. – Вип. 4(41). – С. 34–41. 12. Grant M. CVX: MATLAB software for disciplined convex programming, version 2.0 beta / M. Grant, Boyd S // [Electronic resource]. – Access mode: http://cvxr.com/cvx.

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