On Dropout Modelling for Stability Analysis of Networked Control Systems

This paper presents three discrete-time modelling approaches for networked control systems (NCSs) that incorporate time-varying sampling intervals, time-varying delays and dropouts. The focus of this work is on the extension of two existing techniques to describe dropouts, namely (i) dropouts modelled as prolongation of the delay and (ii) dropouts modelled as prolongation of the sampling interval, and the presentation of a new approach (iii) based on explicit dropout modelling using automata. Based on polytopic overapproximations of the resulting discrete-time NCS models, we provide LMI-based stability conditions for all three approaches. Herewith, we compare the extensions of the existing approaches and the newly proposed method in terms of modelling accuracy, conservatism and complexity of the stability analysis. Using an illustrative example, we provide a thorough numerical comparison of the alternative modelling approaches.