Necessary and Sufficient Conditions for Group Consensus of Agents With Third-Order Dynamics in Directed Networks

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Onur Cihan ◽  
Mehmet Akar
Keyword(s):  
Directed Graph ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Consensus ◽  
Directed Networks ◽  
Third Order ◽  
Systematic Method ◽  
Necessary And Sufficient ◽  
The Given ◽  
Theoretical Results

Abstract In this paper, we investigate the group consensus problem in directed networks where agents have third-order dynamics. Necessary and sufficient conditions on the controller parameters are obtained to ensure K-equilibria group consensus where K is determined by the structure of the directed graph. It is theoretically shown that, for an arbitrary directed graph, there exist controller parameters that satisfy the given conditions. A systematic method for choosing the controller parameters to guarantee group consensus is suggested and theoretical results are verified by numerical examples.

scholarly journals Full idempotents in Leavitt path algebras

2019 ◽  
Vol 18 (04) ◽  
pp. 1950062
Author(s):  
Ekrem Emre
Keyword(s):  
Directed Graph ◽  
Sufficient Conditions ◽  
Path Algebra ◽  
Necessary And Sufficient Conditions ◽  
Leavitt Path Algebra ◽  
Path Algebras ◽  
Leavitt Path Algebras ◽  
Necessary And Sufficient

We give necessary and sufficient conditions on a directed graph [Formula: see text] for which the associated Leavit path algebra [Formula: see text] has at least one full idempotent. Also, we define [Formula: see text] sub-graphs of [Formula: see text] and show that [Formula: see text] has at least one full idempotent if and only if there is a sub-graph [Formula: see text] such that the associated Leavitt path algebra [Formula: see text] has at least one full idempotent.

scholarly journals Hypersurface Family with a Common Isoasymptotic Curve

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ergin Bayram ◽  
Emin Kasap
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Necessary And Sufficient ◽  
The Given

We handle the problem of finding a hypersurface family from a given asymptotic curve in R4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. We illustrate this method by presenting some examples.

scholarly journals Consensus Analysis for Third-Order Multiagent Systems in Directed Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yanfen Cao ◽  
Yuangong Sun
Keyword(s):  
Dynamical Systems ◽  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Consensus Problem ◽  
Third Order ◽  
Consensus Analysis ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Theoretical Results

We investigate consensus problem for third-order multiagent dynamical systems in directed graph. Necessary and sufficient conditions to consensus of third-order multiagent systems have been established under three different protocols. Compared with existing results, we focus on the relationship between the scaling strengths and the eigenvalues of the involved Laplacian matrix, which guarantees consensus of third-order multiagent systems. Finally, some simulation examples are given to illustrate the theoretical results.

scholarly journals On nonoscillatory solutions tending to zero of third-order nonlinear differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Ivan Mojsej ◽  
Alena Tartal’ová
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
The Third ◽  
Necessary And Sufficient

Abstract The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.

scholarly journals Oscillation Criteria of Solutions of Third Order Neutral Integro-Differential Equations

2021 ◽  
pp. 3642-3647
Author(s):  
Taghreed Hussein Abed ◽  
Sattar Naser Ketab ◽  
Hussain Ali Mohamad
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Necessary And Sufficient

      Some necessary and sufficient conditions are obtained that guarantee the oscillation of all solutions of two types of neutral integro-differential equations of third order. The integral is used in the sense of Riemann-Stieltjes. Some examples were included to illustrate the obtained results

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