Comment on Stabilization with guaranteed safety using Control Lyapunov-Barrier Function

Recently, Romdlony and Jayawardhana (2016) proposed control Lyapunov-Barrier functions (CLBFs) for the stabilization of nonlinear control systems while avoiding a bounded set of unsafe states. We demonstrate that CLBFs used in Romdlony and Jayawardhana (2016, Prop. 3 and 5) cannot exist. Critically, this implies that the examples discussed in Romdlony and Jayawardhana (2016) do not satisfy the stated assumptions on CLBFs. (c) 2020 Elsevier Ltd. All rights reserved.