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

Uncertainty Learning for LTI Systems with Stability Guarantees