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A compositional interchange format for hybrid systems is defined in terms of an interchange automaton, allowing arbitrary differential algebraic equations, including fully implicit or switched DAEs, discrete, continuous and algebraic variables, that can be internal or external, urgency conditions, and operators for parallel composition, action hiding, variable hiding and urgent actions. Its compositional semantics is formally defined in terms of a hybrid transition system. This allows development of transformations to and from other formalisms that can be proven to preserve essential properties, and it allows a clear separation between the mathematical meaning of a model and implementation aspects such as algorithms used for solving differential algebraic equations.

Since Pappas et all. transferred the notion of bisimulation from computer science to control theory, it has attracted quite some attention in the hybrid systems community[1]. Notably, bisimulation relations are used to reduce the complexity of dynamic systems, while preserving reachability notions [1]. In [2], we argued that bisimulation needs to be strengthened with continuity conditions, in order to preserve other control science notions as well. This idea was independently explored in [3,4,5] where modal and temporal logics are extended with topological operators, to be able to reason about robustness of a control strategy for embedded systems.

This paper presents an approach to defining distances between nonlinear and hybrid dynamical systems based on formal power series theory. The main idea is that the input-output behavior of a wide range of dynamical systems can be encoded by rational formal power series. Hence, a natural distance between dynamical systems is the distance between the formal power series encoding their input-output behavior. The paper proposes several computable distances for rational formal power series and discusses the application of such distances to various classes of nonlinear and hybrid systems. In particular, the paper presents a detailed discussion of distances for stochastic jump-linear systems.