Convergence analysis of discrete-time consensus algorithm with both self and transmission delays

Multi-agent systems (MAS) are ubiquitous in the real world, typical examples include sensor networks, group robots, and birds flock. Consensus is one of the most typical dynamical behaviors of MAS which implies the states of a group reach some identical value or trajectory asymptotically. It has been widely demonstrated that discrete-time MAS can realize consensus when there does not exist information delay from any node to itself, however, the phenomenon of self delay is possible to occur in cases like sensor aging, actuator delay, or computation incapacity. To characterize such a behavior, this paper introduces an MAS model with dynamically changing topologies by considering both self and transmission delays. Moreover, a simple consensus criterion for such a model is proposed. To prove the correctness of such a criterion, we propose a novel method which is based on the intrinsic relationship between joint and sequential connectivity, it should be noted that such a method does not rely on the widely used Wolfowitz׳s theorem for convergence of infinite products of stochastic matrices.