About second order sliding mode control, relative degree, finite-time convergence and disturbance rejection

The paper deals with twisting and super-twisting along with the discussion about the concept of “High Order Sliding Mode Control”. Lyapunov function is designed to demonstrate, first, asymptotic stability and then finite time convergence for the systems with bounded disturbances.

[1]  Alexander S. Poznyak,et al.  Lyapunov function design for finite-time convergence analysis: "Twisting" controller for second-order sliding mode realization , 2009, Autom..

[2]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[3]  Jaime A. Moreno,et al.  A linear framework for the robust stability analysis of a Generalized Super-Twisting Algorithm , 2009, 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE).

[4]  A. Zinober Variable Structure and Lyapunov Control , 1994 .

[5]  V. Utkin Variable structure systems with sliding modes , 1977 .

[6]  Arie Levant,et al.  Homogeneity approach to high-order sliding mode design , 2005, Autom..

[7]  V. I. Utokin Variable Structure System with Sliding Mode , 1978 .

[8]  Y. ORLOV,et al.  Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems , 2004, SIAM J. Control. Optim..

[9]  Petar V. Kokotovic,et al.  Singular perturbations and order reduction in control theory - An overview , 1975, at - Automatisierungstechnik.

[10]  B. Draenovi The invariance conditions in variable structure systems , 1969 .

[11]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[12]  Arie Levant,et al.  Principles of 2-sliding mode design , 2007, Autom..

[13]  B. Drazenovic,et al.  The invariance conditions in variable structure systems , 1969, Autom..

[14]  A. Levant Sliding order and sliding accuracy in sliding mode control , 1993 .