Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions

2021/04/29 by Laurent Boudin, Francesco Salvarani, Boudin, Laurent +3
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2104.14183

openalex publication_date 2021/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows to define a weighted mean corresponding to the consensus, and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate.

Related

• Convergence to consensus of the general finite-dimensional Cucker-Smale\n model with time-varying delays
• Convergence to consensus in multiagent systems and the lengths of inter-communication intervals
• Lyapunov Approach to Consensus Problems
• A simple consensus model for an increasing population of agents with i.i.d incoming opinions
• Convergence of type-symmetric and cut-balanced consensus seeking systems (extended version)