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BIBO stability of continuous and discrete -time systems

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A new approach to the stability analysis of continuous-time distributed consensus algorithms.

Bo Liu¹, Wenlian Lu, Tianping Chen

¹Key Laboratory of Nonlinear Mathematics Science, School of Mathematical Sciences, Fudan University, Shanghai, PR China. liu7bo9@gmail.com

Neural Networks : the Official Journal of the International Neural Network Society

|July 9, 2013

Summary

We present a novel method for analyzing distributed consensus algorithms in networks with changing communication patterns. This approach converts continuous-time systems into discrete-time models, yielding more general convergence results for network stability.

Keywords:

Almost sure convergence Consensus Discontinuous Distributed algorithms Multiagent systems Switching

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Area of Science:

Control Theory
Networked Systems
Distributed Algorithms

Background:

Consensus algorithms are crucial for distributed systems, enabling agreement among agents.
Analyzing stability in continuous-time systems with dynamic networks is challenging.
Existing methods often rely on continuous-time Lyapunov functions, limiting applicability.

Purpose of the Study:

To develop a new, more general approach for stability analysis of distributed continuous-time consensus algorithms.
To address challenges posed by time-dependent communication patterns in directed networks.
To provide an alternative analysis method to existing continuous-time Lyapunov function approaches.

Main Methods:

Conversion of continuous-time consensus algorithms to equivalent discrete-time models.
Stability analysis of the resulting discrete-time system.
Utilizing the discrete-time model to derive convergence properties.

Main Results:

A novel method for stability analysis of continuous-time consensus algorithms is established.
The proposed method yields a more general convergence result compared to existing literature.
The approach is effective even with time-dependent communication patterns in directed networks.

Conclusions:

The conversion to a discrete-time model offers a powerful and more general framework for analyzing consensus algorithm stability.
This method overcomes limitations of traditional continuous-time Lyapunov-based analyses.
The findings are validated through a numerical simulation example, demonstrating practical applicability.