An arbitrary-order differentiator design paradigm with adaptive gains

References

• Bacciotti, A. , & Rosier, L . (2005). Lyapunov functions and stability in control theory (2nd ed.). Berlin: Springer-Verlag.
   Google Scholar
• Banks, S. P. , & Mhana, K. J. (1992). Optimal control and stabilization for nonlinear systems. IMA Journal of Mathematical Control and Information , 9 , 179–196.
   Web of Science ®Google Scholar
• Boyd, S. , El Ghaoui, L. , Feron, E. , & Balakrishnan, V . (1994). Linear matrix inequalities in system and control theory , Studies in Applied Mathematics , (Vol. 15 ). Philadelphia, PA: SIAM.
   Google Scholar
• Chawda, V. , Celik, O. , O’Malley, M . (2011, June). Application of Levant's differentiator for velocity estimation and increased Z-width in haptic interfaces. In World haptics conference (WHC), 2011 (pp. 403–408). Piscataway: IEEE.
   Google Scholar
• Cruz-Zavala, E. , & Moreno, J. A. (2016). Lyapunov functions for continuous and discontinuous differentiators. IFAC-PapersOnLine , 49 , 660–665.
   Google Scholar
• Cruz-Zavala, E. , Moreno, J. A. , & Fridman, L. M. (2011). Uniform robust exact differentiator. IEEE Transactions on Automatic Control , 56 , 2727–2733.
   Web of Science ®Google Scholar
• Davila, A. , Moreno, J. A. , Fridman, L. M . (2009, December). Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm. In 48th IEEE conference on decision and control (pp. 8405–8410). Piscataway, NJ: IEEE.
   Google Scholar
• Kobayashi, S. , & Furuta, F. (2007). Frequency characteristics of Levant's differentiator and adaptive sliding mode differentiator. International Journal of Systems Science , 38 , 825–832.
   Web of Science ®Google Scholar
• Langson, W. , & Alleyne, A . (1999). A stability result with application to nonlinear regulation: Theory and experiments. In Proceedings of the American control conference (Vol. 5, pp. 3051–3056). Piscataway, NJ: IEEE.
   Google Scholar
• Langson, W. , & Alleyne, A. (2002). A stability result with application to nonlinear regulation. Journal of Dynamic Systems, Measurement, and Control , 124 , 452–456.
   Web of Science ®Google Scholar
• Levant, A. (1998). Robust exact differentiation via sliding mode technique. Automatica , 34 , 379–384.
   Web of Science ®Google Scholar
• Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control , 76 , 924–941.
   Web of Science ®Google Scholar
• Levant, A. (2005). Homogeneity approach to high-order sliding mode design. Automatica , 41 , 823–830.
   Web of Science ®Google Scholar
• Livne, M. , & Levant, A. (2014). Proper discretization of homogeneous differentiators. Automatica , 50 , 2007–2014.
   Web of Science ®Google Scholar
• Moreno, J . (2009, January). A linear framework for the robust stability analysis of a Generalized Super-Twisting Algorithm. In 6th International conference on electrical engineering, computing science and automatic control, CCE (pp. 1–6). Piscataway, NJ: IEEE.
   Google Scholar
• Moreno, J. , & Osorio, M. (2012). Strict lyapunov functions for the super-twisting algorithm. IEEE Transactions on Automatic Control , 57 , 1035–1040.
   Web of Science ®Google Scholar
• Moreno, J. , Osorio, M . (2008, December). A Lyapunov approach to second-order sliding mode controllers and observers. In 47th IEEE conference on decision and control (pp. 2856–2861). Piscataway, NJ: IEEE.
   Google Scholar
• Moreno, J. A . (2012). Lecture notes in control and information sciences. Lyapunov approach for analysis and design of second order sliding mode algorithms. In L. Fridman , J. Moreno & R. Iriarte (Eds.), Sliding modes after the first decade of the 21st century (pp. 113–149). Berlin: Springer-Verlag.
   Google Scholar
• Oliveira, T. R. , Estrada, A. , Fridman, L . (2015, December). Global exact differentiator based on higher-order sliding modes and dynamic gains for globally stable output-feedback control. In 2015 54th IEEE conference on decision and control (CDC) (pp. 4109–4114). Piscataway, NJ: IEEE.
   Google Scholar
• Oliveira, T. R. , Estrada, A. , Fridman, L . (2016, June). Output-feedback generalization of Variable Gain Super-Twisting Sliding Mode Control via global HOSM differentiators. In 2016 14th international workshop on variable structure systems (VSS) (pp. 257–262). Piscataway, NJ: IEEE.
   Google Scholar
• Orani, N. , Pisano, A. , Usai, E . (2006, December). On a new sliding-mode differentiation scheme. In IEEE international conference on industrial technology, 2006. ICIT 2006 (pp. 2652–2657). Piscataway, NJ: IEEE.
   Google Scholar
• Orlov, Y . (2009). Discontinuous systems: Lyapunov analysis and robust synthesis under uncertainty conditions . London: Springer-Verlag.
   Google Scholar
• Orlov, Y. , Aoustin, Y. , & Chevallereau, C. (2011). Finite time stabilization of a perturbed double integrator - Part I: Continuous sliding mode-based output feedback synthesis. IEEE Transactions on Automatic Control , 56 , 614–618.
   Web of Science ®Google Scholar
• Ortiz-Ricardez, F. A. , Sanchez, T. , & Moreno, J. A . (2015, December). Smooth Lyapunov function and gain design for a second order differentiator. In 54th IEEE conference on decision and control (CDC) (pp. 5402–5407). Piscataway, NJ: IEEE.
   Google Scholar
• Pisano, A., Usai, E. (2011). Sliding mode control: A survey with applications in math. Mathematics and Computers in Simulation. Important aspects on structural dynamical systems and their numerical computation , 81 , 954–979.
   Google Scholar
• Plestan, F. , Shtessel, Y. , Bregeault, V. , & Poznyak, A. (2010). New methodologies for adaptive sliding mode control. International Journal of Control , 83 , 1907–1919.
   Web of Science ®Google Scholar
• Polyakov, A. , & Poznyak, A. (2009). Reaching time estimation for super-twisting second order sliding mode controller via Lyapunov function designing. IEEE Transactions on Automatic Control , 54 , 1951–1955.
   Web of Science ®Google Scholar
• Shtessel, Y. , Edwards, C. , Fridman, L. , & Levant, A . (2014). Sliding mode control and observation . New York, NY: Birkhäuser.
   Google Scholar
• Shtessel, Y. , Taleb, M. , & Plestan, F. (2012). A novel adaptive-gain supertwisting sliding mode controller: Methodology and application. Automatica , 48 , 759–769.
   Web of Science ®Google Scholar
• Shtessel, Y. B. , Moreno, J. , Plestan, F. , Fridman, L. M. , Poznyak, A . (2010, December). Super-twisting adaptive sliding mode control: A Lyapunov design. In 49th IEEE conference on decision and control (CDC) (pp. 5109–5113). Piscataway, NJ: IEEE.
   Google Scholar
• Sidhom, L. , Pham, M. T. , Thévenoux, F. , & Gautier, M . (2010, July). Identification of a robot manipulator based on an adaptive higher order sliding modes differentiator. In International conference on advanced intelligent mechatronics, IEEE/ASME (pp. 1093–1098).
   Google Scholar
• Sidhom, L. , Smaoui, M. , Thomasset, D. , Brun, X. , & Bideaux, E . (2011). Adaptive higher order sliding modes for two-dimensional derivative estimation. In 18th IFAC World congress (Vol. 44, pp. 3063–3071). Oxford, UK: Elsevier Ltd.
   Google Scholar