Analysis of Two-Dimensional Feedback Systems Over Networks Using Dissipativity

This paper investigates the closed-loop L-2 stability of two-dimensional (2-D) feedback systems across a digital communication network by introducing the tool of dissipativity. First, sampling of a continuous 2-D system is considered and an analytical characterization of the QSR-dissipativity of the sampled system is presented. Next, the input-feedforward output-feedback passivity, a simplified form of QSR-dissipativity, is utilized to study the framework of feedback interconnection of two 2-D systems over networks. Then, the effects of signal quantization in communication links on dissipativity degradation of the 2-D feedback quantized system is analyzed. Additionally, an event-triggered mechanism is developed for 2-D networked control systems while maintaining L-2 stability of the closed-loop system. In the end, an illustrative example is provided.