TY - GEN
T1 - Stability of discrete-time Altafini's model
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
AU - Liu, Ji
AU - Chen, Xudong
AU - Basar, Tamer
AU - Belabbas, Mohamed Ali
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - This paper considers the discrete-time version of Altafini's model for opinion dynamics in which the interaction among a group of agents is described by a time-varying signed digraph. Prompted by an idea from [1], stability of the system is studied using a graphical approach. Necessary and sufficient conditions for exponential stability with respect to each possible type of limit states are provided. Specifically, under appropriate assumptions, it is shown that (1) a certain type of two-clustering will be reached exponentially fast for almost all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two-clustering; (2) the system will converge to zero exponentially fast for all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally unbalanced.
AB - This paper considers the discrete-time version of Altafini's model for opinion dynamics in which the interaction among a group of agents is described by a time-varying signed digraph. Prompted by an idea from [1], stability of the system is studied using a graphical approach. Necessary and sufficient conditions for exponential stability with respect to each possible type of limit states are provided. Specifically, under appropriate assumptions, it is shown that (1) a certain type of two-clustering will be reached exponentially fast for almost all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two-clustering; (2) the system will converge to zero exponentially fast for all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally unbalanced.
UR - https://www.scopus.com/pages/publications/84962019014
U2 - 10.1109/CDC.2015.7402646
DO - 10.1109/CDC.2015.7402646
M3 - Conference contribution
AN - SCOPUS:84962019014
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2835
EP - 2840
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 15 December 2015 through 18 December 2015
ER -