Distributed PD Average Consensus of Lipschitz Nonlinear MASs in the Presence of Mixed Delays

In this work, the distributed average consensus for dynamical networks with Lipschitz nonlinear dynamics is studied, where the network communication switches quickly among a set of directed and balanced switching graphs. Differing from existing research concerning uniform constant delay or time-varying delays, this study focuses on consensus problems with mixed delays, equipped with one class of delays embedded within the nonlinear dynamics and another class of delays present in the control input. In order to solve these problems, a proportional and derivative control strategy with time delays is proposed. In this way, by using Lyapunov theory, the stability is analytically established and the conditions required for solving the consensus problems are rigorously derived over switching digraphs. Finally, the effectiveness of the designed algorithm is tested using the MATLAB R2021a platform.