Digital control of continuous-time switching systems with safety constraints

Relations between safe sets for a continuous-time switching system S and an appropriate discrete-time switching system associated with S are established. Exploiting these relations, the maximal controlled invariant set for the continuous-time switching system can be arbitrarily closely approximated by an appropriate controlled invariant set for the discretized switching system. Moreover, the safety control problem in a continuous time domain is reduced to a safety problem in a discrete time domain.