Quadric Inclusion Programs: An LMI Approach to $\mathcal H_\infty$-Model Identification.

Practical application of $\mathcal H_\infty$ robust control relies on the system identification of a valid model set, described by a linear system in feedback with a stable norm-bounded uncertainty. This model set should explain all possible (or at least all previously measured) behavior for the controlled plant. Such models can be viewed as norm-bounded inclusions in the frequency domain. This note introduces the “quadric inclusion program” that can identify inclusions from the input–output data as a convex problem. We prove several key properties of this algorithm and give a geometric interpretation for its behavior. While we stress that the inclusion fitting is outlier sensitive by design, we offer a method to mitigate the effect of measurement noise. We apply this method to robustly approximate the simulated frequency-domain data using orthonormal basis functions. The result compares favorably with a least squares approach that satisfies the same data inclusion requirements. [ABSTRACT FROM AUTHOR]