Consensus problem of the first-order linear network and the second-order linear network

Consensus problem have a long history in the field of computer science, particularly in automata theory and distributed computation. And in our life, consensus also an important role. In this article, we focus on the first-order linear consensus network with time-delay and the second-order linear consensus network with time-delay. We find out the solvability of asymptotic consensus for a network with time-delay using the Linear Matrix Inequality (LMI) technology, the Lyapunov stability theorem and the frequency-domain knowledge.