Probabilistic Estimates for Mixed Model Validation Problems With ${cal H}_{\infty }$ Type Uncertainties

A mixed deterministic/probabilistic model validation problem is investigated in this technical note, which consists in an additive uncertain model with model uncertainty characterized by the H_∞ norm. The data available for validation are time-domain experimental data corrupted by a random noise sequence. Our aim is to compute the probability for such an uncertain model to be validated by the data, and our main results are bounds on this probability that are computable based on the distribution of Chi-square random variables when the noise is a Gaussian variable, and solvable as an LMI problem when only statistical information such as the expectation and covariance of the noise are known.