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Robust consensus for uncertain multi‐agent systems with discrete‐time dynamics
Author(s) -
Han Dongkun,
Chesi Graziano
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2968
Subject(s) - mathematics , double integrator , upper and lower bounds , lyapunov function , discrete time and continuous time , robust control , semidefinite programming , multi agent system , convex optimization , mathematical optimization , linear matrix inequality , polynomial , consensus , function (biology) , adjacency matrix , set (abstract data type) , computer science , regular polygon , discrete mathematics , control system , nonlinear system , artificial intelligence , mathematical analysis , graph , engineering , biology , geometry , quantum mechanics , evolutionary biology , statistics , physics , electrical engineering , programming language
SUMMARY This paper investigates robust consensus for multi‐agent systems with discrete‐time dynamics affected by uncertainty. In particular, the paper considers multi‐agent systems with single and double integrators, where the weighted adjacency matrix is a polynomial function of uncertain parameters constrained into a semialgebraic set. Firstly, necessary and sufficient conditions are provided for robust consensus based on the existence of a Lyapunov function polynomially dependent on the uncertainty. In particular, an upper bound on the degree required for achieving necessity is provided. Secondly, a necessary and sufficient condition is provided for robust consensus with single integrator and nonnegative weighted adjacency matrices based on the zeros of a polynomial. Lastly, it is shown how these conditions can be investigated through convex programming by exploiting linear matrix inequalities and sums of squares of polynomials. Some numerical examples illustrate the proposed results. Copyright © 2013 John Wiley & Sons, Ltd.