Estimating the region of attraction of uncertain systems with invariant sets

Andrea Iannelli, Andres Marcos, Mark Lowenberg

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

3 Citations (Scopus)
229 Downloads (Pure)


In this article the problem of estimating the Region of Attraction (ROA) for polynomial nonlinear systems subject to modeling uncertainties is studied. Based on recent theoretical studies on the calculation of positively invariant sets, this article proposes an optimization problem which allows robust inner Estimates of the Region of Attraction (rERA) to be evaluated. The uncertainties, which can generically be time-invariant or time-varying, are described as semialgebraic sets, and the problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. The ensuing optimization entails non-convex constraints, and an iterative algorithm to enlarge the provable invariant level set is discussed. The proposed algorithm is applied to two study cases of increasing complexity. Further, in order to benchmark the proposed rERA algorithm, comparisons are shown with a class of well established algorithms based on Lyapunov functions level sets. The results showcase the prowess of the proposed approach and its advantages in terms of accuracy and computational time, particularly as the size of the system increases.
Original languageEnglish
Title of host publicationProceedings of the 9th IFAC Symposium on Robust Control Design (ROCOND 2018)
PublisherElsevier B.V.
Number of pages6
Publication statusPublished - 2018
Event9th IFAC Symposium on Robust Control Design (ROCOND 2018) - Florianópolis, Brazil
Duration: 3 Sep 20185 Sep 2018

Publication series

ISSN (Print)2405-8963


Conference9th IFAC Symposium on Robust Control Design (ROCOND 2018)


  • Region of attraction
  • Uncertain systems
  • Local analysis
  • Sum Of Squares

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