Metrics and topology for nonlinear and hybrid systems

Authors:
Mihály Petreczky;René Vidal
Affiliations:
Center for Imaging Science, Johns Hopkins University, Baltimore, MD;Center for Imaging Science, Johns Hopkins University, Baltimore, MD
Venue:
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Year:
2007

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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.