Identifiability is a property of a parametrization of a system. A parametrization is a map from a parameter set to a parametrized system. It maps parameter values to systems derived from the parametrized system by substituting the parameter values to the parameters. We say that a parametrization is globally identifiable if the parameter values can be uniquely determined from the data which are modeled by the parametrized system. It is structurally identifiable if this holds for almost all parameter values. Therefore verifying structural or global identifiability of a parametrization preceeds determination of numerical values of the parameters. In this paper, we derive necessary and sufficient conditions for the parametrizations of parametrized polynomial and parametrized rational systems to be structurally or globally identifiable. The results are applied to study the identifiability properties of the systems modeling certain biological phenomena.
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Keywords Structural identifiability, Polynomial systems, Rational systems, Algebraic approaches, Realization theory
MSC System identification (msc 93B30), Geometric methods (msc 93B27), Realizations from input-output data (msc 93B15)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher CWI
Series Modelling, Analysis and Simulation [MAS]
Project Realization and control of rational positive systems
Note This work was carried out under project NWO.EW.MATH
Nemcová, J. (2008). Structural identifiability of polynomial and rational systems. Modelling, Analysis and Simulation [MAS]. CWI.