Relating Time Progress and Deadlines in Hybrid Systems

Time progress conditions in hybrid systems are usually speci ed in terms of invariants, predicates characterizing states where time can continuously progress or dually, deadline conditions, predicates characterizing states where time progress immediately stops. The aim of this work is the study of relationships between general time progress conditions and these generated by using state predicates. It is shown that using deadline conditions or invariantsf allows to characterize all practically interesting time progress conditions. The study is performed by using a Galois connection between the corresponding lattices. We provide conditions for the connection to be a homomorphism and apply the results to the compositional description of hybrid systems.