Nonlinear Robust Approaches to Study Stability and Postcritical Behavior of an Aeroelastic Plant

Andrea Iannelli, Andres Marcos, Mark Lowenberg

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

7 Citations (Scopus)
346 Downloads (Pure)


Two approaches to tackle the nonlinear robust stability problem of an aerospace system are compared. The first employs a combination of the describing function method and μ analysis, while the second makes use of integral quadratic constraints (IQCs). The model analyzed consists of an open-loop wing's airfoil subject to freeplay and linear time-invariant parametric uncertainties. The key steps entailed by the application of the two methodologies and their main features are critically discussed. Emphasis is put on the available insight on the nonlinear postcritical behavior known as limit cycle oscillation. It is proposed a strategy to apply IQCs, typically used to find absolute stability certificates, in this scenario, based on a restricted sector bound condition for the nonlinearity. Another contribution of this paper is to understand how the conservatism usually associated with the IQCs multipliers selection can be overcome by using information coming from the first approach. Nonlinear time-domain simulations showcase the prowess of these approaches in estimating qualitative trends and quantitative response's features.

Original languageEnglish
Number of pages14
JournalIEEE Transactions on Control Systems Technology
Early online date15 Jan 2018
Publication statusE-pub ahead of print - 15 Jan 2018


  • Analytical models
  • Describing functions (DFs)
  • integral quadratic constraints (IQCs)
  • Linear systems
  • nonlinear uncertain systems
  • Oscillators
  • robust stability (RS).
  • Robustness
  • Stability criteria
  • Uncertainty

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