Safety guarantee for time-delay systems with disturbances

Time delays occur in various engineering applications because they may be inherent in the plants or caused by networks. In this paper, we investigate the safety verification problem of time-delay systems modeled by nonlinear delay differential equations subject to control inputs and disturbances in their dynamics. Building upon classical control barrier functionals, we develop the notions of input-to-state safety and input-to-state safe control barrier functionals, in which input-to-state safe control barrier functionals are used to guarantee the safety of time-delay systems with control inputs and disturbances. Three examples are provided to demonstrate the proposed approach.