Probabilistic Stabilizability Certificates for a Class of Black-Box Linear Systems

We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems generated by a possibly inexact quantification of some parameters in the state-space matrices. By exploiting a set of realizations of those undetermined parameters, verifying the controlled invariance property of the given set amounts to a linear program, whose feasibility allows us to establish an a-posteriori probabilistic certificate on the controlled invariance property of such a set with respect to the unknown linear time-invariant dynamics. We apply this framework to the control of a networked system with unknown weighted graph.