Stability analysis of a control-theoretic work system model

Cyber-Physical Production Systems (CPPS), with their features such as distributed organization, autonomous control, real-time capability, and intelligent data processing, provide new production planning and control (PPC) capabilities. These possibilities are decisive in a market environment with characterised by smaller batch sizes, a large number of variants and shorter delivery times. However, it is necessary to have early-warning markers to take any measures. In this paper, we deal with a particular control-theoretic model that is capable of simulating a work system, e.g.; a production machine. In particular, the model is able to predict the production duration of all incoming orders and, thus, serves the purpose of improving adherence to schedule of an arbitrary production environment. This paper aims to establish an appropriate stability analysis concept for this specific model. As it turns out, due to the nonlinearity of the model, we want to introduce a mathematically more challenging stability notion, the so-called input-to-state stability.