Feasibility and Regularity Analysis of Safe Stabilizing Controllers under Uncertainty

This paper studies the problem of safe stabilization of control-affine systems under uncertainty. Our starting point is the availability of worst-case or probabilistic error descriptions for the dynamics and a control barrier function (CBF). These descriptions give rise to second-order cone constraints (SOCCs) whose simultaneous satisfaction guarantees safe stabilization. We study the feasibility of such SOCCs and the regularity properties of various controllers satisfying them.