Constructions of strict Lyapunov functions for discrete time and hybrid time-varying systems

Nonlinear Analysis: Hybrid Systems

Volumn 2, Issue 2, 2008, Pages 394-407

  Malisoff, Michael ^a   Mazenc, Frédéric ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b INRIA   (France)

Author keywords

Discrete and hybrid time varying systems; Strict Lyapunov functions

Indexed keywords

EID: 40949165061     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2006.12.005     Document Type: Article

References (27)

1. Albertini F., and Sontag E.D. Continuous control-Lyapunov functions for asymptotically controllable time-varying systems. International Journal of Control 72 (1999) 1630-1641
2. Angeli D. Input-to-state stability of PD-controlled robotic systems. Automatica 35 (1999) 1285-1290
3. Angeli D., and Sontag E.D. Forward completeness, unboundedness observability, and their Lyapunov characterizations. Systems and Control Letters 38 (1999) 209-217
4. Angeli D., Sontag E.D., and Wang Y. A characterization of integral input to state stability. IEEE Transactions on Automatic Control 45 (2000) 1082-1097
5. Bacciotti A., and Rosier L. Liapunov Functions and Stability in Control Theory (2001), Springer, London
6. C. Cai, A. Teel, R. Goebel, Converse Lyapunov theorems and robust asymptotic stability for hybrid systems, in: Proceedings of the 24th American Control Conference, Portand, OR, June 2005, pp. 12-17. http://www.ccec.ece.ucsb.edu/~cai/
7. P. Collins, A trajectory-space approach to hybrid systems, in: Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Katholiek Univ. Leuven, Belgium, August 2004, Paper #250, http://homepages.cwi.nl/~collins/
8. Coron J.-M. Global asymptotic stabilization for controllable systems without drift. Mathematics of Control, Signals & Systems 5 (1992) 295-312
9. Faubourg L., and Pomet J.-B. Control Lyapunov functions for homogeneous Jurdjevic-Quinn systems. ESAIM: Control, Optimisation and Calculus of Variations 5 (2000) 293-311
10. Khalil H. Nonlinear Systems. Third ed. (2002), Prentice-Hall, Englewood Cliffs, NJ
11. Krichman M., Sontag E.D., and Wang Y. Input-output-to-state stability. SIAM Journal on Control and Optimization 39 (2001) 1874-1928
12. M. Malisoff, F. Mazenc, Further constructions of strict Lyapunov functions for time-varying systems, in: Proceedings of the American Control Conference, Portland, OR, June 2005, pp. 1889-1894
13. Malisoff M., and Mazenc F. Further remarks on strict input-to-state stable Lyapunov functions for time-varying systems. Automatica 41 (2005) 1973-1978
14. Mancilla-Aguillar J., Garcia R., Sontag E.D., and Wang Y. On the representation of switched systems with inputs by perturbed control systems. Nonlinear Analysis: Theory, Methods & Applications 60 (2005) 1111-1150
15. Mancilla-Aguillar J., Garcia R., Sontag E.D., and Wang Y. Uniform stability properties of switched systems with switchings governed by digraphs. Nonlinear Analysis: Theory, Methods & Applications 63 (2005) 472-490
16. Mazenc F. Strict Lyapunov functions for time-varying systems. Automatica 39 (2003) 349-353
17. Mazenc F., and Malisoff M. Further constructions of control-Lyapunov functions and stabilizing feedbacks for systems satisfying the Jurdjevic-Quinn conditions. IEEE Transactions on Automatic Control 51 (2006) 360-365
18. F. Mazenc, D. Nesić, Lyapunov functions for time varying systems satisfying generalized conditions of Matrosov theorem, in: Proceedings of the 44th IEEE Conference on Decision & Control (CDC) & European Control Conference ECC 05, Seville, Spain, December 2005, pp. 2432-2437
19. Morin P., Samson C., and Pomet J.-B. Design of homogeneous time-varying stabilizing control laws for driftless systems via oscillatory approximation of Lie brackets in closed loop. SIAM Journal on Control and Optimization 38 (1999) 22-49
20. Nesić D., and Loria A. On uniform asymptotic stability of time-varying parameterized discrete-time cascades. IEEE Transactions on Automatic Control 49 (2004) 875-887
21. Nesić D., Teel A., and Sontag E.D. Formulas relating K L stability estimates of discrete-time and sampled-time nonlinear systems. Systems and Control Letters 38 (1999) 49-60
22. Samson C. Velocity and torque feedback control of a nonholonomic cart. Advanced Robot Control (Grenoble, 1990). Lecture Notes in Control and Information Sciences vol. 162 (1991), Springer, Berlin 125-151
23. Sontag E.D. Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control 34 (1989) 435-443
24. Sontag E.D. Feedback stabilization of nonlinear systems. In: Kaashoek M.A. (Ed). Robust Control of Linear Systems and Nonlinear Control (1990), Birkhäuser, Basel 61-81
25. Sontag E.D., and Wang Y. Notions of input to output stability. Systems and Control Letters 38 (1999) 235-248
26. Sontag E.D., and Wang Y. Lyapunov characterizations of input to output stability. SIAM Journal on Control and Optimization 39 (2001) 226-249
27. Van der Schaft A., and Schumacher H. An Introduction to Hybrid Systems. Lecture Notes in Control and Information Sciences vol. 251 (2000), Springer-Verlag, London