Robustification of Digital Tracking Protocols for Nonlinear Multi-Agent Systems with State Delays

This paper deals with the robust quantized sampled-data consensus tracking problem for nonlinear time-delay Multi-Agent Systems (MASs), affected by actuation disturbances and measurement errors. In particular, a new methodology for the design of robust quantized sampled-data (QSD) controllers achieving the consensus tracking of nonlinear MASs affected by state-delays is proposed. The notion of Steepest Descent Consensus Feedback (SDCF) and the input-to-state stability redesign methodology are used in order to design a new QSD control term able to arbitrarily attenuate the effects of bounded actuation disturbances and suitably bounded measurement errors. Then, it is proved that there exists a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified SDCFs (continuous or not) ensures the consensus tracking in a semi-global practical sense regardless of the above disturbances and errors. Possible discontinuities in the function describing the protocol are also managed. The cases of time-varying sampling intervals and of non-uniform quantization in the input/output channels are included in the theory here developed. The provided results are validated through a numerical example.