Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings

Automatica

Volumn 46, Issue 11, 2010, Pages 1819-1823

  Ma, Ruicheng ^a   Zhao, Jun ^a,b  

^a KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Backstepping; Common Lyapunov function; Global stabilization; Switched nonlinear systems

Indexed keywords

BACKSTEPPING DESIGN; COMMON LYAPUNOV FUNCTIONS; GLOBAL STABILIZATION; STATE FEEDBACK CONTROLLER; SWITCHED NON-LINEAR SYSTEMS; SWITCHING SIGNALS;

CONTROLLERS; DIFFERENTIAL EQUATIONS; FEEDBACK; FEEDBACK CONTROL; LYAPUNOV FUNCTIONS; NONLINEAR CONTROL SYSTEMS; STABILIZATION; STATE FEEDBACK; SWITCHING;

BACKSTEPPING;

EID: 78049251741     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.06.050     Document Type: Article

References (29)

1. A. Astolfi Discontinuous control of nonholonomic systems Systems and Control Letters 27 1 1996 37 45
2. M. Barkhordari Yazdi, and M.R. Jahed-Motlagh Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization Chemical Engineering Journal 155 3 2009 838 843
3. Barkhordari Yazdi, M., Jahed-Motlagh, M. R., Attia, S. A., & Raisch, J. (2009). Switched feedback equivalence of a class of planar switched nonlinear systems. In Proceedings of the 48th IEEE conference on decision and control/the 2009 28th Chinese control conference (pp. 42644269).
4. M.S. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems IEEE Transactions on Automatic Control 43 4 1998 475 482
5. G. Chesi On the minimum stable commutation time for switching nonlinear systems IEEE Transactions on Automatic Control 54 6 2009 1284 1289
6. J. Daafouz, P. Riedinger, and C. Iung Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach IEEE Transactions on Automatic Control 47 11 2002 1883 1887
7. D. Du, B. Jiang, P. Shi, and S. Zhou H∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach IEEE Transactions on Automatic Control 52 8 2007 1520 1525 (Pubitemid 47316704)
8. L. Fainshil, M. Margaliot, and P. Chigansky On the stability of positive linear switched systems under arbitrary switching laws IEEE Transactions on Automatic Control 54 4 2009 897 899
9. R.A. Freeman, and P. Kokotovi Robust nonlinear control design: state-space and Lyapunov techniques 1996 Birkhuser Boston
10. T.-T. Han, S.S. Ge, and T.H. Lee Adaptive neural control for a class of switched nonlinear systems Systems and Control Letters 58 2 2009 109 118
11. J.P. Hespanha, and A.S. Morse Stabilization of nonholonomic integrators via logic-based switching Automatica 35 3 1999 385 393
12. T. Hu, L. Ma, and Z. Lin Stabilization of switched systems via composite quadratic functions IEEE Transactions on Automatic Control 53 11 2008 2571 2585
13. H.K. Khalil Nonlinear systems 3rd ed. 2002 Prentice-Hall New Jersey
14. M. Krstic, I. Kanellakopoulos, and P. Kokotovi Nonlinear and adaptive control design 1995 Wiley-Interscience
15. T.C. Lee, and Z.P. Jiang Uniform asymptotic stability of nonlinear switched systems with an application to mobile robots IEEE Transactions on Automatic Control 53 5 2008 1235 1252
16. D. Liberzon Switching in systems and control 2003 Birkhuser Boston
17. D. Liberzon Lie algebras and stability of switched nonlinear systems V. Blondel, A. Megretski, Unsolved problems in mathematical systems and control theory 2004 Princeton Univ. Press 203 207
18. X. Liu, K. Zhou, and G. Gu Global stabilization of MIMO minimum-phase nonlinear systems without strict triangular conditions Systems and Control Letters 36 5 1999 359 362
19. M. Margaliot Stability analysis of switched systems using variational principles: an introduction Automatica 42 12 2006 2059 2077
20. M. Margaliot, and G. Langholz Necessary and sufficient conditions for absolute stability: the case of second-order systems IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 50 2 2003 227 234
21. R. Marino, and P. Tomei Nonlinear control design: geometric, adaptive, and robust 1995 Prentice-Hall UK
22. P. Mhaskar, N.H. El-Farra, and P.D. Christofides Predictive control of switched nonlinear systems with scheduled mode transitions IEEE Transactions on Automatic Control 50 11 2005 1670 1680 (Pubitemid 41748864)
23. K.S. Narendra, and J. Balakrishnan A common Lyapunov function for stable LTI systems with commuting A-matrices IEEE Transactions on Automatic Control 39 12 1994 2469 2471
24. R. Sepulchre, M. Jankovic, and P. Kokotovi Constructive nonlinear control 1997 Springer London
25. Y. Sharon, and M. Margaliot Third-order nilpotency, nice reachability and asymptotic stability Journal of Differential Equations 233 1 2007 136 150
26. J.-L. Wu Feedback stabilization for multiinput switched nonlinear systems: two subsystems case IEEE Transactions on Automatic Control 53 4 2008 1037 1042
27. J.-L. Wu Stabilizing controllers design for switched nonlinear systems in strict-feedback form Automatica 45 4 2009 1092 1096
28. J. Zhao, and D.J. Hill On stability, L 2 -gain and H∞ control for switched systems Automatica 44 5 2008 1220 1232
29. Zhao, S., & Zhao, J. (2004). Global stabilization of a class of cascade switched nonlinear systems. In Proceedings of the 43rd IEEE conference on decision and control (pp. 28172822).