  This paper investigates the closed-loop $\mathcal{L}_2$ 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 (IF-OFP), 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
$\mathcal{L}_2$ stability of the closed-loop system. In the end, an
illustrative example is provided.
