# Controller design and region of attraction estimation for nonlinear dynamical systems

arXiv: https://arxiv.org/abs/1310.2213 · HTML: https://mlsanity.com/paper/1310.2213/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2013.

## Built on by (most cited first, 1 of 1)

- [Improving the Region of Attraction of a Multi-rotor UAV by Estimating Unknown Disturbances](https://mlsanity.com/paper/2409.00257/) (2024)

## Abstract (arXiv)

This work presents a method to obtain inner and outer approximations of the region of attraction of a given target set as well as an admissible controller generating the inner approximation. The method is applicable to constrained polynomial dynamical systems and extends to trigonometric and rational systems. The method consists of three steps: compute outer approximations, extract a polynomial controller while guaranteeing the satisfaction of the input constraints, compute inner approximations with respect to the closed-loop system with this controller. Each step of the method is a convex optimization problem, in fact a semidefinite program consisting of minimizing a linear function subject to linear matrix inequality (LMI) constraints. The inner approximations are positively invariant provided that the target set is included in the inner approximation and/or is itself invariant. %The approach readily extends to trigonometric dynamics and/or constraints.