Alhassan, Mohammed Kamil2020-02-032020-02-032020-012020-012020-01-31http://hdl.handle.net/11693/52985Cataloged from PDF version of article.Thesis (M.S.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2020.Includes bibliographical references (leaves 66-69).We discuss consensus problems under time delays. The presence of time delays results in an infinite-dimensional system rather than a system of ordinary differential equations. It has been shown that information transmission delays do not influence whether the system converges to a consensus value; however, further effects of delays are unknown. We show that time delays in most graphs decreases the convergence speed; while somewhat surprisingly, they can improve convergence in certain special graphs. We discuss the structure of graphs for which such improvement is possible.xi, 69 leaves : charts ; 30 cm.Englishinfo:eu-repo/semantics/openAccessConsensus problemsTime delaysConvergence speedUndirected graphsDirected graphsGraph operationsNormalized laplacianStabilityThesisB105367