An extension of the structured singular value to nonlinear systems with application to robust flutter analysis

Andrea Iannelli*, Mark H Lowenberg , Andres Marcos

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
58 Downloads (Pure)


The paper discusses an extension of mu (or structured singular value), a well-established technique from robust control for the study of linear systems subject to structured uncertainty, to nonlinear polynomial problems. Robustness is a multifaceted concept in the nonlinear context, and in this work the point of view of bifurcation theory is assumed. The latter is concerned with the study of qualitative changes of the steady-state solutions of a nonlinear system, so-called bifurcations. The practical goal motivating the work is to assess the effect of modeling uncertainties on flutter, a dynamic instability prompted by an
adverse coupling between aerodynamic, elastic, and inertial forces, when considering the system as nonlinear. Specifically, the onset of flutter in nonlinear systems is generally associated with limit cycle oscillations emanating from a Hopf bifurcation point. Leveraging mu and its complementary modeling paradigm, namely linear fractional transformation, this work proposes an approach to compute margins to the occurrence of Hopf bifurcations for uncertain nonlinear systems. An application to the typical section case study with linear unsteady aerodynamic and hardening nonlinearities in the structural parameters will be presented to demonstrate the applicability of the approach.
Original languageEnglish
Pages (from-to)1057–1069 (2020)
Number of pages14
JournalCEAS Aeronautical Journal
Early online date9 Sept 2020
Publication statusE-pub ahead of print - 9 Sept 2020


  • Bifurcation
  • Robust control
  • Flutter
  • Modeling uncertainties


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