Metrics and Topology for Nonlinear and Hybrid Systems

Abstract. 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.

• Type: Conference
• Year: 2007
• Where: HYBRID
• Authors: Mihály Petreczky, René Vidal
• Keywords: Dynamical Systems, Formal Power Series, HYBRID 2007, Hybrid Systems, Rational Formal Power