  We present a framework for learning of modeling uncertainties in Linear Time
Invariant (LTI) systems. We propose a methodology to extend the dynamics of an
LTI (without uncertainty) with an uncertainty model, based on measured data, to
improve the predictive capacity of the model in the input-output sense. The
proposed framework guarantees stability of the extended model. To achieve this,
two semi-definite programs are provided that allow obtaining optimal
uncertainty model parameters, given state and uncertainty data. To obtain this
data from available input-output trajectory data, we introduce a filter in
which an internal model of uncertainty is proposed. This filter is also
designed via a semi-definite program with guaranteed robustness with respect to
uncertainty model mismatches, disturbances, and noise. Numerical simulations
are presented to illustrate the effectiveness and practicality of the proposed
methodology in improving model accuracy, while warranting model stability.
