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Articles

On simple scheme of finite/fixed-time control designFootnote*

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Pages 1353-1361 | Received 16 Jan 2018, Accepted 23 Jul 2018, Published online: 13 Aug 2018

References

  • Andrieu, V., Praly, L., & Astolfi, A. (2008). Homogeneous Approximation, Recursive Observer Design, and Output Feedback. SIAM Journal on Control and Optimization, 47(4), 1814–1850. doi: 10.1137/060675861
  • Angulo, M. T., Moreno, J. A., & Fridman, L. (2013). Robust exact uniformly convergent arbitrary order differentiator. Automatica, 49, 82489–2495. doi: 10.1016/j.automatica.2013.04.034
  • Bacciotti, A., & Rosier, L. (2005). Lyapunov functions and stability in control theory. Berlin: Springer.
  • Bernuau, E., Polyakov, A., Efimov, D., & Perruquetti, W. (2013). Verification of ISS, iISS and IOSS properties applying weighted homogeneity. System and Control Letters, 62(12), 1159–1167. doi: 10.1016/j.sysconle.2013.09.004
  • Bhat, S. P., & Bernstein, D. S. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal of Control and Optimization, 38(3), 751–766. doi: 10.1137/S0363012997321358
  • Chernousko, F. L., Ananevskii, I. M., & Reshmin, S. A. (2008). Control of nonlinear dynamical systems: Methods and applications. Berlin: Springer-Verlag.
  • Cruz-Zavala, E., & Moreno, J. A. (2017). Homogeneous high order sliding mode design: A Lyapunov approach. Automatica, 80, 232–238. doi: 10.1016/j.automatica.2017.02.039
  • Dorling, C. M., & Zinober, A. S. I. (2007). Two approaches to hyperplane design in multivariable variable structure control systems. International Journal of Control, 44(1), 65–82. doi: 10.1080/00207178608933583
  • Efimov, D., Levant, A., Polyakov, A., & Perruquetti, W. (2017). Supervisory acceleration of convergence for homogeneous systems. International Journal of Control, 1–11. doi: 10.1080/00207179.2017.1415465
  • Efimov, D., Polyakov, A., Perruquetti, W., & Richard, J.-P. (2016). Weighted homogeneity for time-delay systems: Finite-time and independent of delay stability. IEEE Transactions on Automatic Control, 61(1), 210–215. doi: 10.1109/TAC.2015.2427671
  • Filippov, A. (1988). Differential equations with discontinuous right-hand sides. Dordrecht: Springer Netherlands.
  • Harmouche, M., Laghrouche, S., Chitour, Y., & Hamerlain, M. (2016). Stabilisation of perturbed chains of integrators using Lyapunov-based homogeneous controllers. International Journal of Control, 90(12), 2631–2640.
  • Isidori, A. (1995). Nonlinear control systems. London: Springer-Verlag.
  • Levant, A., & Dvir, Y. (2014). Accelerated high-order MIMO sliding mode control. Proceedings of the 13th international workshop on variable structure systems, Nantes, France (pp. 1–6). doi:10.1109/VSS.2014.6881095
  • Orlov, Y. (2004). Finite time stability and robust control synthesis of uncertain switched systems. SIAM Journal of Control and Optimization, 43(4), 1253–1271. doi: 10.1137/S0363012903425593
  • 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(3), 614–618. doi: 10.1109/TAC.2010.2090708
  • Polyakov, A. (2012). Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 57(8), 2106–2110. doi: 10.1109/TAC.2011.2179869
  • Polyakov, A., Efimov, D., & Perruquetti, W. (2015). Finite-time and fixed-time stabilization: Implicit Lyapunov function approach. Automatica, 51, 332–340. doi: 10.1016/j.automatica.2014.10.082
  • Polyakov, A., Efimov, D., & Perruquetti, W. (2016). Robust stabilization of MIMO systems in finite/fixed time. International Journal of Robust and Nonlinear Control, 26, 169–90. doi: 10.1002/rnc.3297
  • Sanchez, T., & Moreno, J. (2013). On a sign controller for the triple integrator. Proceedings of the 52nd annual conference on decision and control (CDC), Florence, Italy (pp. 3566–3571). doi:10.1109/CDC.2013.6760431
  • Su, Y., & Zheng, C. (2015). Robust finite-time output feedback control of perturbed double integrator. Automatica, 60, 86–91. doi: 10.1016/j.automatica.2015.07.008
  • Trivedi, P., & Bandyopadhyay, B. (2011). Finite-time stabilization of uncertain triple integrator with only switch and gain. Proceedings of the 37th annual conference on IEEE Industrial Electronics Society (IECON 2011), Melbourne, VIC, Australia (pp. 3942–3946).
  • Utkin, V., Guldner, J., & Shi, J. (2009). Sliding mode control in electro-mechanical systems. London: CRC Press.
  • Zimenko, K., Efimov, D., Polyakov, A., & Perruquetti, W. (2017). A note on delay robustness for homogeneous systems with negative degree. Automatica, 79, 178–184. doi: 10.1016/j.automatica.2017.01.036
  • Zimenko, K., Polyakov, A., & Efimov, D. (2016). Stabilization of chain of integrators with arbitrary order in finite-time. Proceedings of the 54th IEEE conference on decision and control, Osaka, Japan (pp. 4637–4641).
  • Zimenko, K., Polyakov, A., Efimov, D., & Perruquetti, W. (2018). Finite-time and fixed-time stabilization for integrator chain of arbitrary order. European Control Conference (ECC 2018), Limassol, Cyprus (pp. 1631–1635).
  • Zubov, V. (1958). On systems of ordinary differential equations with generalized homogeneous right-hand sides. (in Russian). Izvestia vuzov. Mathematica, 1, 80–88.

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