Model invalidation for repeated ℓ1-bounded linear time-varying uncertainty models

Conditions are derived for the existence of a repeated linear time-varying (LTV) ℓ₁-bounded perturbation and some ℓ_∞-bounded disturbance signals that are able to describe experimental data. The uncertainty structure is motivated by formation control problems where complex dynamic systems with similar dynamics are moving together and safety can be measured in terms of the relative distances. It is shown that by solving linear programming problems a disturbance-perturbation trade-off curve useful for unfalsified robust performance computation can be determined. The invalidation results are demonstrated on the simulation example of a homogeneous vehicle platoon.