Compositional and Assume-Guarantee Reasoning for Switching Linear Systems

Modular modeling techniques play an important role in the analysis of engineering processes as well as in control applications. While individual components of aggregated models can be relatively simple, complexity increases significantly when interconnections are considered. To address the problem of complexity explosion, simulation relations can be employed to abstract system behaviors by lower order models. As an application to formal verification, simulation relations allow to check system properties such as safety requirements. In a compositional framework, they can be used to approximate interconnections of systems based on approximations of the individual components. While results with regard to compositional analysis have been presented for discrete and recently also for continuous-time systems, it is our aim to develop compositional and assume-guarantee reasoning for a specific class of hybrid systems, namely switching linear systems.