A Lyapunov approach to second-order sliding mode controllers and observers

• Published in: 2008 47th IEEE Conference on Decision and Control pp. 2856 - 2861
• Main Authors: Moreno, J.A., Osorio, M.
• Format: Conference Proceeding
• Language: English; Japanese
• Published: IEEE 2008
• Subjects: Algorithm design and analysis; Convergence; Error correction; Frequency; Lyapunov method; Robust control; Robust stability; Robustness; Sliding mode control; Uncertainty
• ISBN: 9781424431236; 1424431239
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2008.4739356

In this paper a strong Lyapunov function is obtained, for the first time, for the super twisting algorithm, an important class of second order sliding modes (SOSM). This algorithm is widely used in the sliding modes literature to design controllers, observers and exact differentiators. The introduction of a Lyapunov function allows not only to study more deeply the known properties of finite time convergence and robustness to strong perturbations, but also to improve the performance by adding linear correction terms to the algorithm. These modification allows the system to deal with linearly growing perturbations, that are not endured by the basic super twisting algorithm. Moreover, the introduction of Lyapunov functions opens many new analysis and design tools to the higher order sliding modes research area.