Stability analysis of networked control systems with periodic protocols and uniform quantizers

The presence of a communication network in a control loop induces imperfections, such as quantization effects, packet dropouts, time-varying transmission intervals, time-varying transmission delays and communication constraints. The objectives of this paper are to provide a unifying modeling framework that incorporates all these imperfections, and to present novel techniques for the stability analysis for these networked control systems (NCSs). We focus on linear plants, linear controllers and periodic protocols, which leads to a modeling framework for NCSs based on discrete-time switched linear uncertain systems. Using an overapproximated system in the form of a polytopic model with additive norm-bounded uncertainty, we use LMI-based techniques to analyze the input-to-state stability (ISS) of the obtained NCS models with respect to the norm-bounded additive disturbances on plant and controller signals induced by quantization. These ISS conditions will be used to assess closed-loop stability and performance for periodic communication protocols and uniform quantizers, although the framework allows for extensions towards other types of protocols and other types of quantizers as well. We illustrate the effectiveness of the developed theory on a benchmark example of a batch reactor.