Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

Mehdi Imani Masouleh, David J.N. Limebeer

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.

Original languageEnglish
Pages (from-to)1118-1138
Number of pages21
JournalVehicle System Dynamics
Issue number7
Publication statusPublished - 3 Jul 2018
Externally publishedYes


  • Lyapunov stability
  • nonlinear stability analysis
  • rational tyre model
  • Region of attraction
  • sum-of-squares programming
  • vehicular lateral dynamics

ASJC Scopus subject areas

  • Automotive Engineering
  • Safety, Risk, Reliability and Quality
  • Mechanical Engineering


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