Results on solution sets to hybrid systems with applications to stability theory

Proceedings of the American Control Conference

Volumn 1, Issue , 2005, Pages 557-562

  Goebel, R ^a,c   Teel, A R ^b  

^a University of California ^*  (United States)

^b University of California   (United States)

^c Center for Control Engineering and Computation   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; TIME DOMAIN ANALYSIS;

GRAPHICAL CONVERGENCE; HYBRID SYSTEMS; SOLUTION SETS;

SET THEORY;

EID: 23944489962     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (32)

1. Z. Artstein. Invariant measures of differential inclusions applied to singular perturbations. J. Diff. Eq., 152:289-307, 1999.
2. Z. Artstein and A. Vigodner. Singularly perturbed ordinary differential equations with dynamic limits. Proc Royal Society of Edinburgh, 126A:541-569, 1996.
3. J.-P. Aubin. Viability theory. Birkhauser, 1991.
4. J.-P. Aubin and A. Cellina. Differential Inclusions. Springer-Verlag, 1984.
5. J.-P. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube. Impulse differential inclusions: a viability approach to hybrid systems. IEEE Trans. Automat. Control, 47(1):2-20, 2002.
6. A. Bacciotti and L. Rosier. Liapunov Functions and Stability in Control Theory, volume 267 of Lecture Notes in Control and Information Sciences. Springer Verlag, 2001.
7. M. Broucke and A. Arapostathis. Continuous selections of trajectories of hybrid systems. Systems & Control Lett., 47:149-157, 2002.
8. C. Cai, A.R. Teel, and R. Goebel. Converse Lyapunov theorems and robust asymptotic stability for hybrid systems. In Proc 24th American Control Conference, 2005.
9. F.H. Clarke, Y.S. Ledyaev, and R.J. Stern. Asymptotic stability and smooth Lyapunov functions. J. Diff. Eq., 149(1):69-114, 1998.
10. P. Collins. A trajectory-space approach to hybrid systems. In 16th International Symposium on Mathematical Theory of Networks and Systems, 2004.
11. R. Goebel, J. Hespanha, A. Teel, C. Cai, and R. Sanfelice. Hybrid systems: generalized solutions and robust stability. In Stuttgart Symposium on Nonliear Control Systems, 2004.
12. I.A. Hiskens and M.A. Pai. Trajectory sensitivity analysis of hybrid systems. IEEE Trans. Circuits Syst - Part I: Fund. Theory and Apps., 47(2):204-220, 2000.
13. K.H. Johansson, M. Egerstedt, J. Lygeros, and S. Sastry. On the regularization of Zeno hybrid automata. Systems & Control Letters. 38:141-150, 1999.
14. C.M. Kellett. Advances in converse and control Lyapunov functions. PhD thesis, University of California, Santa Barbara, 2002.
15. C.M. Kellett and A.R. Teel. Smooth Lyapunov functions and robustness of stability for difference inclusions. Systems & Control Letters, 52:395-405, 2004.
16. H.K. Khalil. Nonlinear Systems. Prentice-Hall, 3rd edition, 2002.
17. N. N. Krasovskii. Problems of the theory of stability of motion. Stanford Univ. Press, 1963. Translation of Russian edition, Moscow 1959.
18. J. P. LaSalle. An invariance principle in the theory of stability. In Differential equations and dynamical systems. New York: Academic Press, 1967.
19. J. P. LaSalle and S. Lefschetz. Stability by Lyapunov s direct method. New York: Academic Press. 1961.
20. Y.S. Ledyaev and E.D. Sontag. A Lyapunov characterization of robust stabilization. Nonlinear Analysis, 37:813-840, 1999.
21. J. Lygeros, K.H. Johansson, S. Sastry, and M. Egerstedt. On the existence of executions of hybrid automata. In Proc 38th IEEE Conference on Decision and Control, Phoenix, 1999, pages 22492254, 1999.
22. J. Lygeros, K.H. Johansson, S.N. Simić, J. Zhang, and S.S. Sastry. Dynamical properties of hybrid automata. IEEE Trans. Automat. Control. 48(1):2-17, 2003.
23. A.N. Michel and B. Hu. Towards a stability theory of general hybrid dynamical systems. Automatica, 35(3):371-384, 1999.
24. C. Prieur. Perturbed hybrid systems, applications in control theory. In A. Zinober and D. Owens, editors. Nonlinear and adaptive control, volume 281 of Lecture Notes in Control and Inform. Sci., pages 285-294. Springer, Berlin, 2003.
25. C. Prieur and A. Astolfi. Robust stabilization of chained systems via hybrid control. IEEE Trans. Automat. Control, 48(10): 1768-1772, 2003.
26. R.T. Rockafellar and R. J-B Wets. Variational Analysis. Springer, 1998.
27. E.P. Ryan. An integral invariance principle for differential inclusions with applications in adaptive control. SIAM J. Control Optim., 36(3):960-980, 1998.
28. R.G. Sanfelice, R. Goebel, and A.R. Teel. Results on convergence in hybrid systems via detectability and an invariance principle. In Proc. 24th American Control Conference, 2005.
29. L. Tavernini. Differential automata and their discrete simulators. Nonlinear Anal., 11(6):665-683, 1987.
30. A.R. Teel, L. Moreau, and D. Nesic. A unified framework for input-to-state stability in systems with two time scales. IEEE Transactions on Automatic Control, 48(9): 1526-1544, 2003.
31. A.R. Teel and L. Praly. A smooth Lyapunov function from a class-KL estimate involving two positive semidefinite functions. ESAIM Control Optim. Calc. Var., 5:313-367, 2000.
32. A. van der Schaft and H. Schumacher. An Intruduction to Hybrid Dynamical Systems, volume 251 of Lect. Notes in Contr. and Inform. Sci. Springer, 2000.