Robust hypothesis testing for structured uncertainty models

Developing uncertainty models suitable for modern Tobust design methods involves numerous modeling decisions regarding uncertainty structure, noise models and uncertainty bounds. In this paper, we consider the problem of selecting between one of two candidate uncertainty models based on input-output data. Each uncertainty model consists of a nominal linear plant with a standard linear fractional transformation (LFT) uncertainty structure and Gaussian output noise. A classical statistical hypothesis testing performance measure is used to evaluate decision procedures. We derive a D-scaled upper bound on this performance measure, and show that this upper bound can be minimized by convex programming and H_∞ filtering techniques. In addition, a general robust hypothesis testing result is derived.