Assume-guarantee reasoning for linear dynamical systems

The notion of simulation relation has been adopted from theoretical computing science to control theory to reduce the complexity arising in modeling physical processes. Simulations can serve as an abstraction of a given system behavior whilst preserving the input-output structure. We intend to apply simulation relations to develop a framework for compositional and assume-guarantee reasoning for linear dynamical systems. The underlying idea is to use information about the relation of components or subsystems to abstract the behavior of interconnected systems. The interconnection structure is hereby defined by two types of negative feedback.