Sensitivity matrices as keys to local structural system properties of large-scale nonlinear systems

L.G. Van Willigenburg*, J.D. Stigter, J. Molenaar

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Sensitivities are shown to play a key role in a highly efficient algorithm, presented in this paper, to establish three fundamental structural system properties: local structural identifiability, local observability, and local strong accessibility. Sensitivities have the advantageous property to be governed by linear dynamics, also if the system itself is nonlinear. By integrating their linear dynamics over a short time period, and by sampling the result, a sensitivity matrix is obtained. If this sensitivity matrix satisfies a rank condition, then the local structural system property under investigation holds. This rank condition will be referred to in this paper as the sensitivity rank condition (SERC). Applying a singular value decomposition (SVD) to the sensitivity matrix not only determines its rank but also pinpoints exactly the system components causing a possible failure to satisfy the local structural system property. The algorithm is highly efficient because integration of linear systems over short time-periods and computation of an SVD are computationally cheap. Therefore, it allows for the handling of large-scale systems in the order of seconds, as opposed to conventional algorithms that mostly rely on Lie series expansions and a corresponding Lie algebraic rank condition (LARC). The SERC and LARC algorithms are mathematically and computationally compared through a series of examples.

Original languageEnglish
Pages (from-to)2599-2618
JournalNonlinear Dynamics
Issue number3
Early online date29 Jan 2022
Publication statusPublished - Feb 2022


  • Large-scale nonlinear systems
  • Lie algebraic rank condition (LARC)
  • Local controllability
  • Local observability
  • Local strong accessibility
  • Local structural identifiability
  • Sensitivity matrix
  • Sensitivity rank condition (SERC)
  • Singular value decomposition


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