Application of the LISS Lyapunov-Krasovskii small-gain theorem to autonomously controlled production networks with time-delays

Abstract

Abstract-In this paper we consider general autonomously controlled production networks. A production network consists of geographically distributed plants, which are connected by transport routes such that transportation times (time-delays) have to be taken into account. In autonomous controlled production networks logistic objects (e.g., parts, orders) route themselves through a network based on local information. In this paper these kinds of logistic networks are investigated in view of stability to avoid negative outcomes such as high inventory costs or loss of customers. We use the local inputto-state stability (LISS) property and the tool of an LISS Lyapunov-Krasovskii functional for the stability investigation. By the application of the LISS Lyapunov-Krasovskii small-gain theorem we derive conditions, which guarantee stability of the production network.

Autonomous and Central Control of Production Networks

“…It was shown in [11] that if each subsystem of an interconnected system with timedelays admits a LR or a LK function(al) and if the small-gain condition (12) is satisfied, then the whole network possesses the ISS property. A certain scenario of an autonomously controlled production network was investigated using the mentioned tools in [6,7].…”

The stability study of time-delay system based on Lyapunov-Razumikhn

“…Reference [5] in which the Lyapunov-Razumikhin equation is solved for control system stability by constructing the Lyapunov-Razumikhin equation. The stability of time-delay system is discussed in the reference [3] in terms of Lyapunov-Razumikhin equation and Lyapunov-Krasovskii equation respectively. However, because of the existence of variable time-delay in real systems, scholars at home and abroad have directed their attention to the study of variable time-delay.But a large part of them focus on the method of linear matrix inequality [1,4,6].…”