Realization Theory for Discrete-Time Semi-algebraic Hybrid Systems

Authors:
Mihály Petreczky;René Vidal
Affiliations:
Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB and Center for Imaging Science, Johns Hopkins University, Baltimore, USA MD 21218;Center for Imaging Science, Johns Hopkins University, Baltimore, USA MD 21218
Venue:
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Year:
2008

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Abstract

We present realization theory for a class of autonomous discrete-time hybrid systems called semi-algebraic hybrid systems. These are systems in which the state and output equations associated with each discrete state are defined by polynomial equalities and inequalities. We first show that these systems generate the same output as semi-algebraic systems and implicit polynomial systems. We then derive necessary and almost sufficient conditions for existence of an implicit polynomial system realizing a given time-series data. We also provide a characterization of the dimension of a minimal realization as well as an algorithm for computing a realization from a given time-series data.