A discrete-time framework for stability analysis of nonlinear networked control systems

In this paper we develop a prescriptive framework for the stabilising controller design based on approximate discrete-time models for nonlinear Networked Control Systems (NCSs) with time-varying sampling intervals, potentially large time-varying delays and packet dropouts. As opposed to emulation-based approaches where the effects of sampling-and-hold and delays are ignored in the phase of controller design, we propose an approach in which the controller design is based on approximate discrete-time models constructed for a nominal (non-zero) sampling interval and a nominal delay while taking into account sampling-and-hold effects. Subsequently, sufficient conditions for the global exponential stability and semi-global practical asymptotic stability of the closed-loop NCS are provided. These results represent extensions to the existing literature in several ways. Firstly, the results presented in this paper extend results on the controller design for nonlinear sampled-data systems (with constant sampling intervals and no delays) based on approximate discrete-time models to the case of nonlinear sampled-data systems with delays and to the case of NCSs with uncertainties on the sampling intervals and delays. From a different perspective, the results in this paper extend the results on discrete-time modelling and stability analysis for linear NCSs with time-varying sampling intervals, delays and packet dropouts to the realm of nonlinear systems. The results are illustrated by means of examples.