# Gap Metric Robustness of Adaptive Controllers

French, Mark (2002) Gap Metric Robustness of Adaptive Controllers. In, Mathematical Theory of Networks and Systems, Notre Dame, IN,

We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the (linear) $L^2[0,\infty)$ gap metric. The gap perturbations may be more constrained for larger disturbances and for larger parametric uncertainty. Working within the framework of the nonlinear gap metric [3], universal adaptive controllers are first given achieving this goal for first order plants, and the results are then generalised to relative degree one, minimum phase plants.