  To improve the predictive capacity of system models in the input-output
sense, this paper presents a framework for model updating via learning of
modeling uncertainties in locally (and thus also in globally) Lipschitz
nonlinear systems. First, we introduce a method to extend an existing known
model with an uncertainty model so that stability of the extended model is
guaranteed in the sense of set invariance and input-to-state stability. To
achieve this, we provide two tractable semi-definite programs. These programs
allow obtaining optimal uncertainty model parameters for both locally and
globally Lipschitz nonlinear models, given uncertainty and state trajectories.
Subsequently, in order to extract this data from the available input-output
trajectories, we introduce a filter that incorporates an approximated internal
model of the uncertainty and asymptotically estimates uncertainty and state
realizations. This filter is also synthesized using semi-definite programs with
guaranteed robustness with respect to uncertainty model mismatches,
disturbances, and noise. Numerical simulations for a large data-set of a roll
plane model of a vehicle illustrate the effectiveness and practicality of the
proposed methodology in improving model accuracy, while guaranteeing stability.
