Compositional construction of abstractions via relaxed small-gain conditions Part II: discrete case

This paper investigates the compositional construction of approximately bisimilar abstractions for incrementally input-to-state stable (δ-ISS) networks of systems. Toward this end, we develop small-gain conditions which can be applied to networks whose subsystems are not necessarily individually δ-ISS. In contrast to existing results, our method for the compositional construction of the abstractions does not assume that each subsystem is individually δ-ISS. The effectiveness of our results is illustrated via an example.