# Analysis of Two-Dimensional Feedback Systems over Networks Using Dissipativity

## TL;DR

This paper develops a dissipativity-based framework to analyze the stability of two-dimensional feedback systems over networks, considering sampling, quantization, and event-triggered control.

## Contribution

It introduces a novel dissipativity analysis approach for 2-D systems over networks, including sampling, quantization effects, and event-triggered mechanisms.

## Key findings

- Analytical characterization of $QSR$-dissipativity for sampled 2-D systems.
- Framework for feedback interconnection of 2-D systems over networks.
- Event-triggered control maintains stability despite communication constraints.

## Abstract

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.