Stabilization of nonlinear switched systems using control Lyapunov functions

Nonlinear Analysis: Hybrid Systems

Volumn 1, Issue 4, 2007, Pages 482-490

  Moulay, Emmanuel ^a,b   Bourdais, Romain ^a   Perruquetti, Wilfrid ^a  

^a ECOLE CENTRALE DE LILLE   (France)

^b UNIVERSITÉ LILLE 1   (France)

Author keywords

Control Lyapunov function; Nonlinear switched systems; Stabilization

Indexed keywords

EID: 36549017605     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2005.12.001     Document Type: Article

References (14)

1. Liberzon D., and Morse A. Basic problems in stability and design of switched systems. IEEE Control Systems Magazine (1999) 59-70
2. J. Malmborg, Analysis and design of hybrid control systems, Ph.D. Thesis, Lund Instotute of Technology, Sweden, 1998
3. S. Pettersson, B. Lennartson, Stability and robustness for hybrid systems, in: Proceedings of the 35th Conference on Decision and Control, 1996, pp. 1202-1207
4. Branicky M. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control 43 4 (1998) 475-482
5. Mancilla-Aguilar J.L., García R., Sontag E., and Wang Y. On the representation of switched systems with inputs by perturbed control systems. Nonlinear Analysis: Theory, Methods & Applications 60 (2005) 1111-1150
6. Mancilla-Aguilar J.L., and García R. A converse Lyapunov theorem for nonlinear switched systems. Systems & Control Letters 41 (2000) 67-71
7. Vu L., and Liberzon D. Common Lyapunov functions for families of commuting nonlinear systems. Systems & Control Letters 54 (2005) 405-416
8. H. Sun, J. Zhao, Control Lyapunov functions for switched control systems, in: Proceedings of the American Control Conference, Arlington, VA, 2001, pp. 1890-1891
9. Artstein Z. Stabilization with relaxed controls. Nonlinear Analysis: Theory, Methods & Applications 7 11 (1983) 1163-1173
10. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Springer-Verlag, New-York
11. Mickael E. Continuous selections. Analysis Mathematica 63 2 (1956) 361-382
12. Rifford L. On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients. ESAIM Control Optimization and Calculus of Variations 6 (2001) 593-611
13. Lin Y., and Sontag E. A universal formula for stabilization with bounded controls. Systems & Control Letters 16 (1991) 393-397
14. Rifford L. Semiconcave control-Lyapunov functions and stabilizing feedbacks. SIAM Journal on Control and Optimization 41 3 (2002) 659-681