P-stable abstractions of hybrid systems

Abstract

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 \({\mathbb {P}}\)-stable abstractions. Intuitively, the \({\mathbb {P}}\)-stable abstraction of a dynamical system characterizes the transitions between stability regions in response to external inputs. The stability regions are not given—rather, they are synthesized as their most precise representation with respect to a given set of predicates \({\mathbb {P}}\). A \({\mathbb {P}}\)-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 \({\mathbb {P}}\)-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 the algorithm in synthesizing \({\mathbb {P}}\)-stable abstractions for significant systems.