Robustness Analysis of Asynchronous Sampled-Data Multi-Agent Networks With Time-Varying Delays

TL;DR

This paper analyzes the stability of multi-agent networks with asynchronous sampling, delays, and measurement errors, providing new Lyapunov-based criteria for ensuring robustness in practical decentralized control scenarios.

Contribution

It introduces a novel Lyapunov stability framework for asynchronous sampled-data multi-agent systems with delays and errors, applicable to consensus control and robustness analysis.

Findings

Derived maximum allowable sampling periods and delays.

Established stability conditions accommodating measurement errors and quantization.

Extended analysis to systems with input saturations and delays.

Abstract

In this paper, we study the simultaneous stability problem of a finite number of locally inter-connected linear subsystems under practical constraints, including asynchronous and aperiodic sampling, time-varying delays, and measurement errors. We establish a new Lyapunov-based stability result for such a decentralized system. This system has a particular simple structure of interconnections, but it captures some key characteristics of a large class of intermediate models derived from the consensus analysis of multi-agent systems. The stability result is applicable to the estimation of the maximum allowable inter-sampling periods and time delays based on individual dynamics and coupling structures in the scenarios of consensus control via asynchronous sampling of relative states and asynchronous broadcasting of self-sampled states respectively. The asynchrony of aperiodic sampling and the existence of measurement errors allow the utilization of some kinds of quantizing devices, such as Logarithmic quantizers, in the process of data sampling, and allow the introduction of a period of dwell time after each update of state measurement to eliminate the Zeno behavior of events in event-based control. The extension in the case with input saturations and input delays is also discussed.