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.Comment: 6 pages, 5 figures. Accepted for publication at the 2020 American
Control Conference. Copyright IEEE 202