Supervisory acceleration of convergence for homogeneous systems

References

• Ananévskii, I. (2003). Control synthesis for linear systems by methods of stability theory of motion. Difierential Equations , 39 (1), 1–10.
   Web of Science ®Google Scholar
• Ananýevskii, I . (2001). Limited control of a rheonomous mechanical system under uncertainty. Journal of Applied Mathematics and Mechanics , 65 (5), 785–796.
   Web of Science ®Google Scholar
• Bacciotti, A. , & Rosier, L . (2005). Lyapunov functions and stability in control theory (2nd ed.). Berlin: Springer.
   Google Scholar
• Bernuau, E. , Polyakov, A. , Efimov, D. , & Perruquetti, W. (2013). Verification of ISS, iISS and IOSS properties applying weighted homogeneity. Systems & Control Letters , 62 , 1159–1167.
   Web of Science ®Google Scholar
• Bhat, S. P. , & Bernstein, D. S. (2005). Geometric homogeneity with applications to finite-time stability. Mathematics of Control, Signals and Systems , 17 , 101–127.
   Web of Science ®Google Scholar
• Dvir, Y. , & Levant, A. (2015a). Accelerated twisting algorithm. IEEE Transactions on Automatic Control , 60 (10), 2803–2807.
   Web of Science ®Google Scholar
• Dvir, Y. , & Levant, A. (2015b). Sliding mode order and accuracy in sliding mode adaptation and convergence acceleration. In X. Yu M. Önder Efe (Eds.), Recent advances in sliding modes: From control to intelligent mechatronics, volume 24 of Studies in systems, decision and control (pp. 129–153). London: Springer International.
   Google Scholar
• Edwards, C. , & Spurgeon, S. (1998). Sliding mode control: Theory and applications . London: Taylor and Francis.
   Google Scholar
• Efimov, D. , Levant, A. , Polyakov, A. , & Perruquetti, W. (2016). On acceleration of asymptotically stable homogeneous systems. In Proceedings of 55th IEEE CDC . (pp. 7312–7315) . Las Vegas.
   Google Scholar
• Fridman, L . (2011). Sliding mode enforcement after 1990: Main results and some open problems, Vol. 412 of LNCIS (pp. 3–57). Berlin Heidelberg: Springer-Verlag.
   Google Scholar
• Khalil, H.K . (1996). Nonlinear systems . Upper Saddle River, NJ: Prentice-Hall.
   Google Scholar
• Levant, A. (2005). Homogeneity approach to high-order sliding mode design. Automatica , 41 (5), 823–830.
   Web of Science ®Google Scholar
• Lin, Y. , Sontag, E. D. , & Wang, Y. (1996). A smooth converse Lyapunov theorem for robust stability. SIAM Journal on Control and Optimization , 34 (1), 124–160.
   Web of Science ®Google Scholar
• Moreno, J. , & Osorio, A. (2012). Strict Lyapunov functions for the super-twisting algorithm. IEEE Transactions on Automatic Control , 57 (4), 1035–1040.
   Web of Science ®Google Scholar
• Moulay, E. , & Perruquetti, W. (2006). Finite time stability and stabilization of a class of continuous systems. Journal of Mathematical Analysis and Application , 323 (2), 1430–1443.
   Web of Science ®Google Scholar
• Moulay, E. , & Perruquetti, W. (2008). Finite time stability conditions for non autonomous continuous systems. International Journal of Control , 81 (5), 797–803.
   Web of Science ®Google Scholar
• Polyakov, A. (2012). Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control , 57 (8), 2106–2110.
   Web of Science ®Google Scholar
• Poznyak, A. , Fridman, L. , & Bejarano, F.J. (2004). Mini-max integral sliding-mode control for multimodel linear uncertain systems. IEEE Transactions on Automatic Control , 49 (1), 97–102.
   Web of Science ®Google Scholar
• Roxin, E. (1966). On finite stability in control systems. Rendiconti del Circolo Matematico di Palermo , 15 , 273–283.
   Google Scholar
• Utkin, V.I . (1992). Sliding modes in control optimization . Berlin: Springer-Verlag.
   Google Scholar
• Zubov, V . (1958). On systems of ordinary differential equations with generalized homogenous right-hand sides. Izvestia vuzov Mathematica , 1 , 80–88 ( in Russian).
   Google Scholar