Robust estimations of the Region of Attraction using invariant sets

Andrea Iannelli*, Andres Marcos, Mark Lowenberg

*Corresponding author for this work

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

14 Citations (Scopus)
130 Downloads (Pure)


The Region of Attraction of an equilibrium point is the set of initial conditions whose trajectories converge to it asymptotically. This article, building on a recent work on positively invariant sets, deals with inner estimates of the ROA of polynomial nonlinear dynamics. The problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. Numerical issues related to the ensuing optimization are discussed and strategies to tackle them are proposed. These range from the adoption of different iterative methods to the reduction of the polynomial variables involved in the optimization. The main contribution of the work is an algorithm to perform the ROA calculation for systems subject to modeling uncertainties, and its applicability is showcased with two case studies of increasing complexity. Results, for both nominal and uncertain systems, are compared with a standard algorithm from the literature based on Lyapunov function level sets. They confirm the advantages in adopting the invariant sets approach, and show that as the size of the system and the number of uncertainty increase, the proposed heuristics ameliorate the commented numerical issues.
Original languageEnglish
Pages (from-to)4622-4647
Number of pages26
JournalJournal of the Franklin Institute
Issue number8
Early online date15 Feb 2019
Publication statusPublished - 1 May 2019


  • Region of attraction
  • Local analysis
  • Uncertainties
  • Sum of squares
  • Nonlinear dynamics
  • Robust analysis

Cite this