Control Barrier Functions in Sampled-Data Systems

This letter presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness sufficient on controllers. Then, propose three approaches guaranteeing invariance, motivated by continuous-time barrier functions, one discrete-time functions. All proposed are control affine, thus can be incorporated into quadratic programs synthesis. We show that less conservative than those in earlier studies, via simulation how this enables use functions impossible implement desired time-step using existing methods.