Synthesis of P-Stable Abstractions

Stability is a fundamental requirement of dynamical systems. Most of the works concentrate on verifying stability for a given stability region. In this paper we tackle the problem of synthesizing -stable abstractions. Intuitively, the-stable abstraction of an open dynamical system characterizes the transitions between stability regions in response to external inputs. The stability regions are not given - rather, they are synthesized as the tightest representation with respect to a given set of relevant predicates. A stable abstraction is enriched by timing information derived from the duration of stabilization. We implement a synthesis algorithm in the framework of Abstract Interpretation, that allows different degrees of approximation. We show the representational power of stable abstractions, that provide a high-level account of the behavior of the system with respect to stability, and we experimentally evaluate the effectiveness of a compositional approach, that allows synthesizing stable abstractions for significant systems.