Stability analysis of networked and quantized linear control systems

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 simultaneously, and to present novel techniques for the stability analysis for these networked control systems (NCSs). In contrast to many other papers that consider quantization in NCSs, we incorporate quantization effects in the modeling framework by modeling them as norm-bounded additive disturbances on both plant and controller signals. We focus on linear plants and controllers, and periodic and quadratic 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 propose LMI-based techniques to analyze the input-to-state stability (ISS) and the ℓ2ℓ2-gain properties of the obtained NCS models with respect to the norm-bounded additive disturbances induced by quantization. These ISS and ℓ2ℓ2-gain conditions will be used to assess closed-loop stability and performance for two classes of quantizers. We illustrate the effectiveness of the developed theory on a benchmark example of a batch reactor.