Gap Metric Robustness of Adaptive Controllers

Abstract

We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the (linear) L²(0,∞) 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.

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