Exponentially stable solution of mathematical model of agents dynamics on time scales

Abstract This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consensus for any time scale basing on the Grönwall inequality. We give some examples il...

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Main Authors:	Ewa Schmeidel, Urszula Ostaszewska, Małgorzata Zdanowicz
Format:	Article
Language:	English
Published:	SpringerOpen 2019-06-01
Series:	Advances in Difference Equations
Subjects:	Time scales Leader-following problem Grönwall inequality Multi-agent systems Graph theory
Online Access:	http://link.springer.com/article/10.1186/s13662-019-2159-4

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spelling	doaj-dfde9eec38754234b77194cdac8e180f2020-11-25T02:17:09ZengSpringerOpenAdvances in Difference Equations1687-18472019-06-012019111910.1186/s13662-019-2159-4Exponentially stable solution of mathematical model of agents dynamics on time scalesEwa Schmeidel0Urszula Ostaszewska1Małgorzata Zdanowicz2Institute of Mathematics, University of BialystokInstitute of Mathematics, University of BialystokInstitute of Mathematics, University of BialystokAbstract This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consensus for any time scale basing on the Grönwall inequality. We give some examples illustrating the obtained results.http://link.springer.com/article/10.1186/s13662-019-2159-4Time scalesLeader-following problemGrönwall inequalityMulti-agent systemsGraph theory
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ewa Schmeidel Urszula Ostaszewska Małgorzata Zdanowicz
spellingShingle	Ewa Schmeidel Urszula Ostaszewska Małgorzata Zdanowicz Exponentially stable solution of mathematical model of agents dynamics on time scales Advances in Difference Equations Time scales Leader-following problem Grönwall inequality Multi-agent systems Graph theory
author_facet	Ewa Schmeidel Urszula Ostaszewska Małgorzata Zdanowicz
author_sort	Ewa Schmeidel
title	Exponentially stable solution of mathematical model of agents dynamics on time scales
title_short	Exponentially stable solution of mathematical model of agents dynamics on time scales
title_full	Exponentially stable solution of mathematical model of agents dynamics on time scales
title_fullStr	Exponentially stable solution of mathematical model of agents dynamics on time scales
title_full_unstemmed	Exponentially stable solution of mathematical model of agents dynamics on time scales
title_sort	exponentially stable solution of mathematical model of agents dynamics on time scales
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2019-06-01
description	Abstract This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consensus for any time scale basing on the Grönwall inequality. We give some examples illustrating the obtained results.
topic	Time scales Leader-following problem Grönwall inequality Multi-agent systems Graph theory
url	http://link.springer.com/article/10.1186/s13662-019-2159-4
work_keys_str_mv	AT ewaschmeidel exponentiallystablesolutionofmathematicalmodelofagentsdynamicsontimescales AT urszulaostaszewska exponentiallystablesolutionofmathematicalmodelofagentsdynamicsontimescales AT małgorzatazdanowicz exponentiallystablesolutionofmathematicalmodelofagentsdynamicsontimescales
_version_	1724887914623533056

Exponentially stable solution of mathematical model of agents dynamics on time scales

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