Stability Analysis of Large Scale Networks of Autonomous Work Systems with Delays

Abstract

Abstract-This paper considers the problem of stability analysis for a class of production networks of autonomous work systems with delays in the capacity changes. The system under consideration does not share information between work systems and the work systems adjust capacity with the objective of maintaining a desired amount of local work in progress (WIP). Attention is focused to derive explicit sufficient delay-dependent stability conditions for the network using properties of matrix norm. Finally, numerical results are provided to demonstrate the proposed approach.

Trajectory‐based small gain theorems for ISpS and ISS of large‐scale networks of switched systems with arbitrary switchings

“…There are various applications of small gain theorems: works devoted to design of controllers in presence of dynamic uncertainties [2,[12][13][14], works devoted to design of decentralised controllers for multi-agent systems [10], works devoted to stability conditions of the entire network when the stabilisers are already designed based on some physical or engineering considerations and the problem is just to investigate whether the network is stable or not. The latter is applicable, for instance, to logistics [15,16] or to force-reflecting teleoperation systems [17,18].…”

“…Similarly, fix any R 0 * ∈ ]r 0 , r 1 [ and define R q + 1 * := α(R q * ), q ∈ ℤ + and R q − 1 *:= α −1 (R q * ), q ∈ ℤ − . Thus, 0 < r q < R q * < r q + 1 , r q + 1 := α(r q ) and R q + 1 * := α(R q * ) for all q ∈ ℤ(15)and r q → + ∞ as q → + ∞ and r q → + 0 as q → − ∞ (16).…”