Average consensus on strongly connected weighted digraphs: A generalized error bound

This technical communique represents a generalization of the convergence analysis for the consensus algorithm proposed in Priolo et?al. (2014). Although the consensus was reached for any strongly connected weighted digraphs (SCWD), the convergence analysis provided in Priolo et?al. (2014) was only valid for diagonalizable matrices encoding a SCWD. The result we present here generalizes the previous one to all possible matrices encoding a SCWD that can be used in the algorithm.

[1]  Ruggero Carli,et al.  Optimal Synchronization for Networks of Noisy Double Integrators , 2011, IEEE Transactions on Automatic Control.

[2]  Andrea Gasparri,et al.  A distributed algorithm for average consensus on strongly connected weighted digraphs , 2014, Autom..

[3]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[4]  Carlos Sagüés,et al.  Chebyshev Polynomials in Distributed Consensus Applications , 2011, IEEE Transactions on Signal Processing.

[5]  Ling Shi,et al.  Time Synchronization in WSNs: A Maximum-Value-Based Consensus Approach , 2014, IEEE Transactions on Automatic Control.

[6]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[7]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[8]  Jorge Cortés,et al.  Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs , 2009, Eur. J. Control.

[9]  Kai Cai,et al.  Average consensus on general strongly connected digraphs , 2012, Autom..

[10]  Ling Shi,et al.  SATS: Secure Average-Consensus-Based Time Synchronization in Wireless Sensor Networks , 2013, IEEE Transactions on Signal Processing.

[11]  Christoforos N. Hadjicostis,et al.  Distributed strategies for average consensus in directed graphs , 2011, IEEE Conference on Decision and Control and European Control Conference.

[12]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[13]  Frank L. Lewis,et al.  Cooperative control with distributed gain adaptation and connectivity estimation for directed networks , 2014 .