Kybernetika 53 no. 2, 263-281, 2017

Global adaptive output-feedback control for switched uncertain nonlinear systems

Zhibao Song, Junyong Zhai and Hui YeDOI: 10.14736/kyb-2017-2-0263


In this paper, we investigate the problem of global output-feedback regulation for a class of switched nonlinear systems with unknown linear growth condition and uncertain output function. Based on the backstepping method, an adaptive output-feedback controller is designed to guarantee that the state of the switched nonlinear system can be globally regulated to the origin while maintaining global boundedness of the resulting closed-loop switched system under arbitrary switchings. A numerical example is given to demonstrate the effectiveness of the proposed control scheme.


adaptive control, switched nonlinear system, output-feedback


93D21, 39A13


  1. A. Bacciotti and L. Rosier: Lyapunov Functions and Stability in Control Theory. Springer, New York 2005.   DOI:10.1007/b139028
  2. M. Branicky: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Control 43 (1998), 475-482.   DOI:10.1109/9.664150
  3. N. El-Farra, P. Mhaskar and P. Christofides: Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Syst. Control Lett. 54 (2005), 1163-1182.   DOI:10.1016/j.sysconle.2005.04.005
  4. M. Krstic, P. Kokotovic and I. Kanellakopoulos: Nonlinear and Adaptive Control Design. John Wiley and Sons, Inc. 1995.   CrossRef
  5. H. Lei and W. Lin: Universal adaptive control of nonlinear systems with unknown growth rate by output feedback. Automatica 42 (2006), 1783-1789.   DOI:10.1016/j.automatica.2006.05.006
  6. H. Lei and W. Lin: Adaptive regulation of uncertain nonlinear systems by output feedback: a universal control approach. Syst. Control Lett. 56 (2007), 529-537.   DOI:10.1016/j.sysconle.2007.03.002
  7. E. Li, L. Long and J. Zhao: Global output-feedback stabilization for a class of switched uncertain nonlinear systems. Appl. Math. Comput. 256 (2015), 551-564.   DOI:10.1016/j.amc.2015.01.039
  8. D. Liberzon and A. Morse: Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19 (1999), 59-70.   DOI:10.1109/37.793443
  9. D. Liberzon: Switching in Systems and Control. Birkhauser, Boston 2003.   DOI:10.1007/978-1-4612-0017-8
  10. L. Long and J. Zhao: Output-feedback stabilization for a class of switched nonlinear systems with unknown control coefficients. Int. J. Control 86 (2013), 386-395.   DOI:10.1080/00207179.2012.733414
  11. J. Wu: Stabilizing controllers design for switched nonlinear systems in strict-feedback form. Automatica 45 (2009), 1092-1096.   DOI:10.1016/j.automatica.2008.12.004
  12. X. Yan and Y. Liu: New results on global output-feedback stabilization for nonlinear systems with unknown growth rate. J. Contr. Theory Appl. 11 (2013), 401-408.   DOI:10.1007/s11768-013-2081-3
  13. B. Yang and W. Lin: Further results on global stabilization of uncertain nonlinear systems by output feedback. Int. J. Robust Nonlinear Control 15 (2005), 247-268.   DOI:10.1002/rnc.985
  14. J. Zhai and C. Qian: Global control of nonlinear systems with uncertain output function using homogeneous domination approach. Int. J. Robust Nonlinear Control 22 (2012), 1543-1561.   DOI:10.1002/rnc.1765
  15. J. Zhai, W. Ai and S. Fei: Global output feedback stabilisation for a class of uncertain non-linear systems. IET Contr. Theory Appl. 7 (2013), 305-313.   DOI:10.1049/iet-cta.2011.0505