Small-gain theorem for safety verification of interconnected systems

A small-gain theorem in the formulation of barrier function is developed in this work for safety verification of interconnected systems. This result is helpful to verify input-to-state safety (ISSf) for interconnected systems from the safety information encoded in the individual ISSf-barrier functions. Also, it can be used to obtain a safety set in a higher dimensional space from the safety sets in two lower dimensional spaces.