Consensus of linear conformable fractional order multi‐agent systems with impulsive control protocols
Jian Guo Yang, Mičhal Fĕckan, JinRong Wang
Abstract
Abstract In this article, we study the impulsive consensus problem of linear multi‐agent systems composed of α ‐order conformable differential equations ( α ∈ (0, 1]). Two cases of fixed and switching interaction networks are considered, respectively. Impulsive protocol of each agent is introduced based on the local information of the interaction networks. Firstly, we derive the analytic solution of the general linear conformable systems with impulses. Secondly, two sufficient criterions are presented to guarantee the convergence of the consistent state for all the agents by using matrix theory, graph theory, and impulsive control theory. Finally, three numerical simulations are provided to demonstrate the obtained theoretical results and to compare the convergence rates of the systems with distinct orders.