Identifying H[infinity]-Models: An LMI Approach.

Practical application of H[infinity] robust control relies on systemidentification of a valid model-set, described by a norm-bounded differentialinclusion, which explains all possible behavior for the control plant. This isusually approximated by measuring the plant repeatedly and finding a model thatexplains all observed behavior. Typical modern approaches must anticipate theuncertainty-shaping aspects of the final model in order to maintaintractability. This paper offers a linear matrix inequality constrainedoptimization for the MIMO model fitting problem that does not require suchknowledge. We do this with a novel "Quadric Inclusion Program" which replacesthe least squares problem in traditional model identification---however ratherthan linear equation models, it returns linear norm-bounded inclusion models.We prove several key properties of this algorithm and give a geometricinterpretation for its behavior. While we stress that the models areoutlier-sensitive by design, we offer a method to mitigate the effect ofmeasurement noise. The paper includes an example of how the theory could beapplied to frequency domain data. Time-domain data could also be used, provideda state vector is constructed from measured signals and their derivatives touse as regressors for a vector of maximal derivatives.