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

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