Uniform Consensus among Self-driven Particles

A nonconservative stability theory for switched linear systems is applied to the convergence analysis of consensus algorithms in the discrete-time domain. It is shown that the uniform-joint-connectedness condition for asymptotic consensus in distributed asynchronous algorithms and multi-particle models is in fact necessary and sufficient for uniform exponential consensus.

[1]  L. Gurvits.  Stability of discrete linear inclusion , 1995 .

[2]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[3]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[4]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[5]  Yang Wang,et al.  Bounded semigroups of matrices , 1992 .

[6]  I. Daubechies,et al.  Sets of Matrices All Infinite Products of Which Converge , 1992 .

[7]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[8]  Ji-Woong Lee,et al.  Uniform stabilization of discrete-time switched and Markovian jump linear systems , 2006, Autom..

[9]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[10]  Geir E. Dullerud,et al.  Optimal Disturbance Attenuation for Discrete-Time Switched and Markovian Jump Linear Systems , 2006, SIAM J. Control. Optim..

[11]  Geir E. Dullerud,et al.  Uniformly Stabilizing Sets of Switching Sequences for Switched Linear Systems , 2007, IEEE Transactions on Automatic Control.

[12]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[13]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[14]  I. Daubechies,et al.  Corrigendum/addendum to: Sets of matrices all infinite products of which converge , 2001 .

[15]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[16]  John N. Tsitsiklis,et al.  Comments on "Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules" , 2007, IEEE Trans. Autom. Control..

[17]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[18]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[19]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.