Robust finite-time output feedback stabilisation of the double integrator

Abstract

The problem of finite-time output stabilisation of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degrees of homogeneity) ensuring the finite-time stabilisation. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. Robustness and effects of discretisation on the closed-loop system obtained are analysed. The efficiency of the solution obtained is demonstrated in computer simulations.

Keywords:

• finite-time stability
• input-to-state stability
• output control
• double integrator

Notes

1. A system is practically stable if there exists an asymptotically stable compact set.

Additional information

Funding

This work was partially supported by the Government of Russian Federation [grant number 074-U01] and the Ministry of Education and Science of Russian Federation (Project 14.Z50.31.0031).