Stability Analysis of Large-Scale Distributed Networked Control Systems with Random Communication Delays: A Switched System Approach

TL;DR

This paper introduces a scalable stability analysis method for large-scale distributed control systems with random delays, using a reduced mode model within a Markov jump linear system framework, and accounts for uncertainties in transition probabilities.

Contribution

A novel reduced mode model for stability analysis of large-scale systems that overcomes scalability issues and handles uncertain transition probabilities.

Findings

The proposed method is computationally efficient for large systems.

It provides bounds for uncertain Markov transition probabilities.

Examples verify the effectiveness of the approach.

Abstract

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump linear system framework. There have been considerable researches on stability analysis of Markov jump systems, however, these methods are not applicable to large-scale systems because large numbers of subsystems result in an extremely large number of the switching modes. To avoid this scalability issue, we propose a new reduced mode model for stability analysis, which is computationally efficient. We also consider the case in which the transition probabilities for the Markov jump process contain uncertainties. We provide a new method that estimates bounds for uncertain Markov transition probability matrix to guarantee the system stability. The efficiency and the usefulness of the proposed methods are verified through examples.