| Abstract: | This paper investigates the consensus problem of second‐order Markovian jump multi‐agent systems with delays. Both network‐induced random delay and node‐induced state delay are considered, where the network‐induced random delay, subjected to a Markov chain, exists in the switching signal and the node‐induced state delay, related to switching topologies, is heterogeneous between any two linked agents. In order to reduce communication and control energy, an impulsive protocol is proposed, where each agent only can get delayed relative positions to neighbors and the velocity of itself at impulsive instants. By performing three steps of model transformation and introducing a mapping for two independent Markov chains, the consensus problem of the original continuous‐time system is equivalent to the stability problem of a discrete‐time expand error system with two Markovian jumping parameters and a necessary and sufficient criterion is derived. A numerical example is given to illustrate the effectiveness of the theoretical result.@@@@This work is supported by the National Natural Science Foundation of China under Grants 61374171, 61572210, and 51537003, the Fundamental Research Funds for the Central Universities (2015TS030), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245). |
