A contraction approach to input tracking via high gain feedback

This paper adopts a contraction approach to study exogenous input tracking in dynamical systems under high gain proportional output feedback. We give conditions under which contraction of a nonlinear system´s tracking error implies input to output stability from the input signal´s time derivatives to the tracking error. This result is then used to demonstrate that the negative feedback connection of plants composed of two strictly positive real subsystems in cascade can follow external inputs with tracking errors that can be made arbitrarily small by applying a sufficiently large feedback gain. We utilize this result to design a biomolecular feedback regulation scheme for a synthetic genetic sensor model, making it robust to variations in the availability of a cellular resource required for protein production.