Robust Dynamic Average Consensus with Bounded Reference Signals Under Directed Networks

Our work considers the dynamic average consensus (DAC) problem for bounded time-varying reference signals under weight-unbalanced directed networks, which is the most general and challenging claim from the perspective of topological structure. Firstly, the conventional surplus-based approach is embedded in the nonsmooth signum function to develop a nonlinear DAC algorithm under unbalanced directed networks. Then, we design a Lyapunov function with perturbation term and use the tools from the nonsmooth analysis as well as the Matrix Perturbation theory to establish convergence properties of the proposed algorithm. Finally, simulation examples and theoretical analysis show that the precise and robust DAC is guaranteed as long as the signals' states and their derivatives are all bounded, which possess the potential in a wider spectrum of application.