Convergence to Zero of Quadratic Lyapunov Functions for Multiagent Systems in Time-Varying Directed Networks

The quadratic Lyapunov function-based method for consensus analysis of discrete-time single-integrator multiagent systems (MASs) in general time-varying directed networks is not well developed, whereas for continuous-time cases remains blank. This note develops this method for both discrete-time and continuous-time MASs with a constant-gain protocol when the network is uniformly strongly connected. By proving the convergence to zero of quadratic Lyapunov functions, we first establish the exponential consensus convergence results for single-integrator MASs in general time-varying directed networks. Then, we show the proposed method can be applied to the consensus analysis of continuous-time MASs with relative-state-dependent noises. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.