Towards composition of conformant systems

Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers both temporal and spatial aspects of the outputs. Previous work developed algorithms for computing the conformance degree between two systems, and demonstrated how formal verification results for one system can be re-used for a system that is conformant to it. In this paper, we study the relation between conformance and a generalized approximate simulation relation for the class of Open Metric Transition Systems (OMTS). This allows us to prove a small-gain theorem for OMTS, which gives sufficient conditions under which the feedback interconnection of systems respects the conformance relation, thus allowing the building of more complex systems from conformant components.