Advanced Studies in Pure Mathematics

Algebraic tools for the analysis of state space models

Nicolette Meshkat, Zvi Rosen, and Seth Sullivant

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We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveying existing algebraic tools for studying ODE systems, we also present a variety of new results. In particular: on structural identifiability, we present a method using linear algebra to find identifiable functions of the parameters of a model for unidentifiable models. On observability, we present techniques using Gröbner bases and algebraic matroids to test algebraic observability of state space models. On indistinguishability, we present a sufficient condition for distinguishability using computational algebra and demonstrate testing indistinguishability.

Article information

The 50th Anniversary of Gröbner Bases, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2018), 171-205

Received: 31 August 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document euclid.aspm/1537499603

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 13P25: Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 05E40: Combinatorial aspects of commutative algebra 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

identifiability observability indistinguishability state space models


Meshkat, Nicolette; Rosen, Zvi; Sullivant, Seth. Algebraic tools for the analysis of state space models. The 50th Anniversary of Gröbner Bases, 171--205, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07710171.

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