An LMI Approach to Exponential Stock Level Estimation for Large-Scale Logistics Networks
This article aims to present a convex optimization approach for exponential stock level estimation problem of large-scale logistics networks. The model under consideration presents the dependency and interconnections between the dynamics of each single location. Using a Lyapunov function, new sufficient conditions for exponential estimation of the networks are driven in terms of linear matrix inequalities (LMIs). The explicit expression of the observer gain is parameterized based on the solvability conditions. A numerical example is included to illustrate the applicability of the proposed design method.
KeywordsStability analysis Logistics networks Estimation LMI
- Dashkovskiy S, Karimi HR, Kosmykov M, Mironchenko A, Naujok L (2010) Application of the LISS Lyapunov-Krasovskii small-gain theorem to autonomously controlled production networks with time-delays. In Proceedings of the conference on control and fault-tolerant systems, pp. 765–770, Nice, FranceGoogle Scholar
- Gahinet P, Nemirovsky A, Laub AJ, Chilali M (1995) LMI control toolbox: for use with matlab. The MATH Works, Inc., NatikGoogle Scholar
- Karimi HR (2008) Observer-based mixed H2/H∝ control design for linear systems with time-varying delays: an LMI approach. Int J Control Autom Sys 6(1):1–14Google Scholar
- Karimi HR, Dashkovskiy S, Duffie NA (2011) Stability analysis of large scale networks of autonomous work systems with delays’: dynamics in logistics. Springer, Heidelberg, pp 69–78Google Scholar
- Weber A (1909) Uber den Standort der Industrien, – translated as Alfred Weber’s theory of location of industries. University of Chicago Press, ChicagoGoogle Scholar