Region of attraction analysis with Integral Quadratic Constraints

Andrea Iannelli*, Peter Seiler, Andrés Marcos

*Corresponding author for this work

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

12 Citations (Scopus)
149 Downloads (Pure)


A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.

Original languageEnglish
Article number108543
Early online date28 Aug 2019
Publication statusPublished - 1 Nov 2019


  • Dissipation inequality
  • Integral quadratic constraints
  • Local analysis
  • Nonlinear uncertain systems
  • Region of attraction


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