Paper: Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems
Automatica (Journal of IFAC)
Brief paper: Estimating the region of attraction for large-scale systems with uncertainties
Automatica (Journal of IFAC)
LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification
International Journal of Robotics Research
Optimal object configurations to minimize the positioning error in visual servoing
IEEE Transactions on Robotics
Automatica (Journal of IFAC)
Nonlinear dynamic systems design based on the optimization of the domain of attraction
Mathematical and Computer Modelling: An International Journal
Estimation of domains of attraction: A global optimization approach
Mathematical and Computer Modelling: An International Journal
Generalised absolute stability and sum of squares
Automatica (Journal of IFAC)
Information Sciences: an International Journal
| Hi-index | 22.15 |
This paper proposes a strategy for estimating the domain of attraction (DA) for non-polynomial systems via Lyapunov functions (LFs). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst-case remainders in truncated Taylor expansions. Moreover, a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen LF, and another condition is provided for establishing whether such an estimate has been found. The proposed strategy can readily be exploited with variable LFs in order to search for optimal estimates. Lastly, it is worth remarking that no other method is available to estimate the DA for non-polynomial systems via LMIs.