Robustness of L1 adaptive controllers in the gap metric

This paper derives robust stability margin of an L₁ adaptive controller in the gap metric. For that purpose, first a classical result on robustness of nonlinear input-output systems is reviewed, and an appropriate extension on biased-gain stability is introduced. This extension circumvents the singularity inherent to the analysis of robustness of adaptive systems, and leads to computable robust stability margin of L₁ adaptive controller. A time-delay margin of the L₁ controller is computed as an illustration of the theoretical results.