Finite-time output stabilization of the double integrator

Verification of ISS, iISS and IOSS properties applying weighted homogeneity

“…Let us consider a planar nonlinear system: 1) are the parameters. Such a system describes dynamics of estimation error when analyzing a finite-time observer/differentiator [28]. In this case d 1 represents the measurement noise and d 2 models an external disturbance or model mismatch.…”

“…In [28] there is also another example, for which a strict Lyapunov function is not known, but using homogeneity it is possible to prove ISS property, it is a nonlinear homogeneous controller from [30].…”

On robustness of a class of homogeneous continuous finite time controllers

“…Reference [14] proves finite time stability of a class of time varying non-linear systems. A recent advance for the finite time stabilisation of a double integrator system can be found in [15] where finite time output feedback was studied without considering robustness to disturbances. Reference [16] proposes a Lyapunov function for the perturbed double integrator, however, the robustness claims are presented without proof.…”

Robust finite-time output feedback control of perturbed double integrator

“…Orlov, Aoustin, and Chevallereau (2011) show that a modification of the twisting controller and the supertwisting observer can be coupled together to present a unified framework for the output feedback finite-time stabilization of a perturbed double integrator. Bernuau, Perruquetti, Efimov, and Moulay (2012) combine a homogeneous observer with a homogeneous control to ensure global finite-time stabilization of the double integrator systems. Other output feedback finite-time stabilizing controls for dynamical systems can be found in Amato, Ariola, and Cosentino (2006), Angulo, Fridman, and Levant (2012), Angulo, Fridman, and Moreno (2013), Dinuzzo and Ferrara (2009), Li and Qian (2006), Li, Qian, and Ding (2010), Plestan, Moulay, Glumineau, and Cheviron (2010) and Qian and Li (2005).…”