Abstract
This paper is dedicated to the double-integrator dynamics subject to antagonistic interaction among participating individuals, apart from the unavailability of the velocity information on the interacting individuals. Unlike the dependence of the signed graph theory and structural balanced theory, eventually positive matrix is used to quantify antagonistic information among participating individuals, upon which the hypothesis of digon sign-symmetry imposed on the signed graph as broadly used in the literature can be entirely got rid of. Moreover, as an application, the “opinion” evolution of the agents is analyzed, and some criteria assuring all agents to share some steady “opinions” are presented. Simulation results are presented to well support the proposed setup and the derived theoretical results.
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