On robustness of stability and Lyapunov functions for discontinuous difference equations

Proceedings of the IEEE Conference on Decision and Control

Volumn 4, Issue , 2002, Pages 4282-4287

  Kellett, Christopher M ^a,b   Teel, Andrew R ^b  

^a PSL RESEARCH UNIVERSITY   (France)

^b University of California at Santa Barbara   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; THEOREM PROVING;

GLOBAL ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS;

ASYMPTOTIC STABILITY;

EID: 0036991720     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. R. P. Agarwal. Difference Equations and Inequalities: Theory, Methods, and Applications. Marcel Dekker, 2 edition, 2000.
2. F. H. Clarke, Y. S. Ledyaev, and R. J. Stern. Asymptotic stability and smooth Lyapunov functions. Journal of Differential Equations, 149:69-114, 1998.
3. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, 1988.
4. Z. Jiang and Y. Wang, A converse Lyapunov theorem for discrete-time systems with disturbances. Systems and Control Letters, 45:49-58, 2002.
5. C. M. Kellett. Advances in Converse and Control Lyapunov Functions. PhD thesis, University of California, Santa Barbara, June 2002.
6. M. Kisielewicz, Differential Inclusions and Optimal Control. Kluwer Academic Publishers, 1991.
7. J. Kurzweil, On the inversion of Ljapunov's second theorem on stability of motion. American Mathematical Society Translations, ser.2, 24:19-77, 1956.
8. Y. Lin, E. D. Sontag, and Y. Wang. A smooth converse Lyapunov theorem for robust stability. SIAM J. Control and Optimization, 34:124-160, 1996.
9. D. Nešić and A. R. Teel, A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. Submitted to IEEE TAC.
10. D. Nešić, A. R. Teel, and P. V. Kokotović, Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Systems and Control Letters, 38:259-270, 1999.
11. E. D. Sontag, Comments on integral variants of ISS. Systems & Control Letters, 34:93-100, 1998.
12. A. Stuart and A. Humphries. Dynamical Systems and Numerical Analysis. Cambridge University Press, 1996.
13. A. R. Teel and L. Praly, A smooth Lyapunov function from a class-KL estimate involving two positive semidefinite functions. ESAIM-Control Optimisation and Calculus of Variations, 5:313-367, 2000.