# Tracking Performance Limitations of MIMO Networked Control Systems with Multiple Communication Constraints

## TL;DR

This paper analyzes the fundamental limits of tracking performance in MIMO networked control systems under various communication constraints, revealing how plant characteristics and noise influence control performance.

## Contribution

It provides an explicit representation of tracking performance limits considering multiple communication constraints and plant properties, including unstable poles and NMP zeros.

## Key findings

- Performance limits depend on plant internal characteristics and noise distribution.
- Angles between NMP zero directions and noise influence tracking accuracy.
- Bandwidth and channel allocation affect performance and can be optimized.

## Abstract

In this paper, the tracking performance limitation of networked control systems (NCSs) is studied. The NCSs is considered as continuous-time linear multi-input multi-output (MIMO) systems with random reference noises. The controlled plants include unstable poles and non-minimum phase (NMP) zeros. The output feedback path is affected by multiple communication constraints. We focus on some basic communication constraints, including additive white noise (AWN), quantization noise, bandwidth, as well as encoder-decoder. The system performance is evaluated with the tracking error energy, and used a two-degree of freedom (2DOF) controller. The explicit representation of the tracking performance is given in this paper. The results indicate the tracking performance limitations rely to internal characteristics of the plant (unstable poles and NMP zeros), reference noises (the reference noise power distribution (RNPD) and its directions) and the characteristics of communication constraints. Moreover, the tracking performance limitations are also affected by the angles between the each transform NMP zero direction and RNPD direction, and these angles between each transform unstable poles direction and the direction of communication constraint distribution/allocation. In addition, for MIMO NCSs, bandwidth (there are not identical two channels) always can affects the direction of unstable poles, and the channel allocation of bandwidth and encode-decode may be used for a feasible method for the performance allocation of each channels. Lastly, a instance is given for verifying the effectiveness of the theoretical outcomes.