The gap metric and its variants play a fundamental role in robust linear control. In an important paper, Georgiou and Smith established a far-reaching generalisation of the gap metric to nonlinear systems. This project initially developed a new approach torobust adaptive control within this robust uncertainty framework.
A second line of research considers the relationship between nonlinear graph topologies and various formulations of the gap metric. In particular relationships between the theory of the gap metric and nonlinear co-prime factorisations have been developed. This is mostly in the context of gain-function notions of stability.