Matrix-scaled Consensus of Network Systems With Uniform Time-delays

Time-delay is an unavoidable factor in analyzing and designing any networked system since in most scenarios, it decreases the performance or even destabilizes the system. In this paper, we study the newly proposed matrix-scaled consensus (MSC) algorithms under the presence of communication time delays. Both networks of single- and double-integrator agents are considered, and for each scenario, a corresponding delay margin will be given. The analysis hinges on the Nyquist stability criteria and the algebraic solution of quasi-polynomials associated with the MSC models. Numerical examples are provided to demonstrate the correctness of theoretical results.