Stabilisation of perturbed chains of integrators using Lyapunov-based homogeneous controllers

References

• Andrieu, V., Praly, L., & Astolfi, A. (2008). Homogeneous approximation, recursive observer and output feedback. SIAM Journal of Control and Optimization, 47(4), 1814–1850.
   Web of Science ®Google Scholar
• Bhat, S., & Bernstein, D. (1997). Finite-time stability of homogeneous systems. In Proceedings of the 1997 American control conference. (Vol. 4, pp. 2513–2514).
   Google Scholar
• Bhat, S., & Bernstein, D. (1998). Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Transactions on Automatic Control, 43(5), 678–682.
   Web of Science ®Google Scholar
• Bhat, S., & Bernstein, D. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal of Control and Optimization, 38(3), 751–766.
   Web of Science ®Google Scholar
• Bhat, S., & Bernstein, D. (2005). Geometric homogeneity with applications to finite-time stability. Mathematics of Control, Signals, and Systems, 17, 101–127.
   Web of Science ®Google Scholar
• Cruz-Zavala, E., Moreno, J., & Fridman, L. (2011). Second-order uniform exact sliding mode control with uniform sliding surface. In 50th IEEE conference on decision and control and European control conference (CDC-ECC) (pp. 4616–4621). IEEE.
   Google Scholar
• Cruz-Zavala, E., Moreno, J., & Fridman, L. (2012). Uniform sliding mode controllers and uniform sliding surfaces. IMA Journal of Mathematical Control and Information, 39(4), 491–505.
   Web of Science ®Google Scholar
• Defoort, M., Floquet, T., Kokosy, A., & Perruquetti, W. (2009). A novel higher order sliding mode control scheme. Systems and Control Letters, 58(2), 102–108.
   Web of Science ®Google Scholar
• Dinuzzo, F., & Fererra, A. (2009). Higher order sliding mode controllers with optimal reaching. IEEE Transactions on Automatic Control, 54(9), 2126–2136.
   Web of Science ®Google Scholar
• Driver, R.D. (1965). Methods of A. M. Lyapunov and their application (V. I. Zubov). SIAM Review, 7(4), 570–571.
   Web of Science ®Google Scholar
• Emel’yanov, S., Korovin, S., & Levant, A. (1996). High-order sliding modes in control systems. Computational Mathematics and Modeling, 7(3), 294–318.
   Google Scholar
• Filippov, A. (1988). Differential equations with discontinuous right-hand side. Dordrecht: Kluwer.
   Google Scholar
• Harmouche, M., Laghrouche, S., & Chitour, Y. (2012). Robust and adaptive higher order sliding mode controllers. In IEEE 51st annual conference on decision and control (CDC) (pp. 6436–6441). IEEE.
   Google Scholar
• Hong, Y. (2002). Finite-time stabilization and stabilizability of a class of controllable systems. Systems and Control Letters, 46(4), 231–236.
   Web of Science ®Google Scholar
• Hong, Y., Wang, J., & Xi, Z. (2005). Stabilization of uncertain chained form systems within finite settling time. IEEE Transactions on Automatic Control, 50(9), 1379–1384.
   Web of Science ®Google Scholar
• Hong, Y., Xu, Y., & Huang, J. (2002). Finite-time control for robot manipulators. Systems and Control Letters, 46(4), 243–253.
   Web of Science ®Google Scholar
• Isidori, A. (1995). Nonlinear control systems: An introduction (3rd ed.). Berlin: Springer.
   Google Scholar
• Kryachkov, M., Polyakov, A., & Strygin, V. (2010). Finite-time stabilization of an integrator chain using only signs of the state variables. In 11th international workshop on variable structure systems (VSS) (pp. 510–515). IEEE.
   Google Scholar
• Levant, A. (2001). Universal single-input– single-output (SISO) sliding-mode controllers with finite-time convergence. IEEE Transactions on Automatic Control, 46(9), 1447–1451.
   Web of Science ®Google Scholar
• Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 76(9/10), 924–941.
   Web of Science ®Google Scholar
• Levant, A. (2005). Homogeneity approach to high-order sliding mode design. Automatica, 41(5), 823–830.
   Web of Science ®Google Scholar
• Li, J., & Qian, C. (2005). Global finite-time stabilization of a class of uncertain nonlinear systems using output feedback. In 44th IEEE conference on decision and control, and 2005 European control conference. CDC-ECC ’05 (pp. 2652–2657). IEEE.
   Google Scholar
• Orlov, Y. (2009). Discontinuous systems – Lyapunov analysis and robust synthesis under uncertainty conditions. London: Springer-Verlag.
   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
• Polyakov, A., & Fridman, L. (2014). Stability notions and Lyapunov functions for sliding mode control systems. Journal of the Franklin Institute, 351(4), 1831–18652012. Advances in Variable Structure Systems and Sliding Mode Algorithms.
   Web of Science ®Google Scholar
• Praly, L. (1997). Generalized weighted homogeneity and state dependent time scale for linear controllable systems. In Proceedings of the 36th IEEE conference on decision and control (Vol. 5, pp. 4342–4347). IEEE.
   Google Scholar
• Qian, C. (2005). A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems. In Proceedings of the 2005 American control conference, 2005 (pp. 4708–4715). IEEE.
   Google Scholar
• Rosier, L. (1992). Homogeneous Lyapunov function for homogeneous continuous vector field. Systems and Control Letters, 19(6), 467–473.
   Web of Science ®Google Scholar
• Zhang, J., Han, Z., & Huang, J. (2013). Homogeneous feedback design of differential inclusions based on control Lyapunov functions. Communications in Nonlinear Science and Numerical Simulation, 18(10), 2790–2800.
   Web of Science ®Google Scholar