Erratum to “A Distributed Algorithm for Average Consensus on Strongly Connected Weighted Digraphs” [Automatica 50 (3) (2014) 946-951] Attilio Priolo a Andrea Gasparri a Eduardo Montijano b,c Carlos Sagues c a Department of Engineering, Roma Tre University, Rome, Italy. b c Centro Universitario de la Defensa (CUD), Zaragoza, Spain. Instituto de Investigaci´ on en Ingenier´ıa de Arag´ on (I3A), Universidad de Zaragoza, Spain. The purpose of this note is to correct Proposition 3 in Priolo et al. (2014), where the diagonalizability of the matrix C needs to be considered in the Assumptions of Proposition 3. More precisely, it should reads as follows. Proposition 3 Let us assume the multi-agent system applies the modified consensus algorithm give in eq. (8) with the Perron matrix C diagonalizable. Then, the disagreement vector ϕ(k) can be bounded as: References A. Priolo, A. Gasparri, E. Montijano, and C. Sagues. A distributed algorithm for average consensus on strongly connected weighted digraphs. Automatica, 50(3):946 – 951, 2014. kϕ(k)k ≤ χ1 k|λC2 |k + χ2 |λC2 |k , with k·k the Euclidean norm and χ1 , χ2 ∈ R two positive constant values. Proof : The proof is the same as presented in Proposition 3 in Priolo et al. (2014), where the diagonalizability of matrix C is used to introduce γ1 in eq.(12). Further, the bound to t211 in the second equation of the right column in page 949 has to be re-derived, and corrected to √ t211 ≤ n (j) − wT (j) 1 ∞ δii (j − 1) − δii (j) √ . ≤ 2 n max |xi (0)| max i i n δii (j) δii (j) | {z } t2111 Thus, the constant χ11 in eq. (14) becomes γ1 1 + χ11 = 2 max |xi (0)| i 1 |λC2 | n d¯2 √ 2 . 2 Email addresses: [email protected] (Attilio Priolo), [email protected] (Andrea Gasparri), [email protected] (Eduardo Montijano), [email protected] (Carlos Sagues). Preprint submitted to Automatica 2 April 2015
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