In this paper, we consider the problem of verifying safety constraint satisfaction for single-input single-output systems with uncertain transfer function coefficients. We propose a new type of barrier function based on a vector norm. This type of barrier function has a measurable upper bound without full state availability. An identifier-based estimator allows an exact bound for the uncertainty-based component of the barrier function estimate. Assuming that the system is safe initially allows an exponentially decreasing bound on the error due to the estimator transient. Barrier function and estimator synthesis is proposed as two convex sub-problems, exploiting linear matrix inequalities. The barrier function controller combination is then used to construct a safety backup controller. And we demonstrate the system in a simulation of a 1 degree-of-freedom human-exoskeleton interaction.
