Mathematical models of nonlinear uniform consensus II

• Main Authors: Saburov, Mansoor, Saburov, Khikmat
• Format: Article
• Language: English; English
• Published: L & H Scientific Publishing, LLC 2018
• Subjects: QA Mathematics; TA Engineering (General). Civil engineering (General)
• Online Access: http://irep.iium.edu.my/64769/1/64769_Mathematical%20models%20of%20nonlinear%20uniform%20consensus%20II_article.pdf; http://irep.iium.edu.my/64769/2/64769_Mathematical%20models%20of%20nonlinear%20uniform%20consensus%20II_scopus.pdf; http://irep.iium.edu.my/64769/; https://www.lhscientificpublishing.com/Journals/JAND-Download.aspx?volume=2018&issue=1
• Institution: Universiti Islam Antarabangsa Malaysia

This paper is a continuation of our previous studies on nonlinear consensus. We have considered a nonlinear protocol for a structured time-invariant and synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of a polynomial stochastic operator associated with a stochastic multidimensional hyper-matrix. We provide a criterion for a uniform consensus in the multi-agent system. Particularly, the uniform consensus is achieved in the multi-agent system if all entries of the stochastic multidimensional hyper-matrix are positive. Some numerical results are also presented to support our theoretical results.