# Characterization of Domain of Fixed-time Stability under Control Input Constraints

arXiv: https://arxiv.org/abs/2004.01540 · HTML: https://mlsanity.com/paper/2004.01540/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2020.

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

- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)

## Abstract (arXiv)

In this paper, we study the effect of control input constraints on the domain of attraction of an FxTS equilibrium point. We first present a new result on FxTS, where we allow a positive term in the time derivative of the Lyapunov function. We provide analytical expressions for the domain of attraction and the settling time to the equilibrium in terms of the coefficients of the positive and negative terms that appear in the time derivative of the Lyapunov function. We show that this result serves as a robustness characterization of FxTS equilibria in the presence of an additive, vanishing disturbances. We use the new FxTS result in formulating a provably feasible quadratic program (QP) that computes control inputs that drive the trajectories of a class of nonlinear, control-affine systems to a goal set, in the presence of control input constraints.