On the continuity of asymptotically stable compact sets for simulations of hybrid systems

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 270-275

  Sanfelice, Ricardo G ^a   Teel, Andrew R ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; COMPUTER SIMULATION; CONFORMAL MAPPING; MATHEMATICAL MODELS;

ASYMPTOTICALLY STABLE COMPACT SETS; BOUNCING BALL SYSTEM;

ASYMPTOTIC ANALYSIS;

EID: 38149121904     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377647     Document Type: Conference Paper

References (25)

1. A. Abate, A. D. Ames, and S. S. Sastry. Error bounds based stochastic approximations and simulations of hybrid dynamical systems. In Proc. 25th American Control Conference, pages 4742-4747, 2006.
2. R. Alur, T. Dang, J. Esposito, Y. Hur, F. Ivancic, V. Kumar, I. Lee, P. Mishra, G. J. Pappas, and O. Sokolsky. Hierarchical modeling and analysis of embedded systems. Proc. of the IEEE, 91:11-28, 2003.
3. U. M. Ascher and L. R. Petzold. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM, 1998.
4. J.-P. Aubin, J. Lygeros, M. Quincampoix, S. S. Sastry, and N. Seube. Impulse differential inclusions: a viability approach to hybrid systems. IEEE Trans. Aut. Cont., 47(1):2-20, 2002.
5. P. Collins. A trajectory-space approach to hybrid systems. In Proc. 16th MTNS, 2004.
6. A. Dontchev and F. Lempio. Difference methods for differential inclusions: A survey. SIAM Review, 34:263-294, 1992.
7. H. Elmqvist, S.E. Mattsson, and M. Otter. Modelica: The new object-oriented modeling language. In Proc. of 12th European Simulation Multiconference, 1998.
8. J.M. Esposito, V. Kumar, and G.J. Pappas. Accurate event detection for simulating hybrid systems. In Hybrid Systems: Computation and Control: 4th International Workshop, pages 204-217, 2001.
9. R. Goebel, J.P. Hespanha, A.R. Teel, C. Cai, and R.G. Sanfelice. Hybrid systems: Generalized solutions and robust stability. In 6th IFAC NOLCOS, pages 1-12, 2004.
10. R. Goebel and A.R. Teel. Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica, 42(4):573-587, 2006.
11. E. Hairer and G. Wanner. Algebraically stable and implementable Runge-Kutta methods of high order. SIAM J. Numer. Anal., 18:1098-1108, 1981.
12. A.R. Humphries and A. M. Stuart. Runge-Kutta methods for dissipative and gradient dynamical systems. SIAM J. Numer. Anal., 31:1452-1485, 1994.
13. E. Kofman. Discrete event simulation of hybrid systems. SIAM Journal on Scientific Computing, 25(5): 1771-1797, 2004.
14. E. A. Lee and H. Zheng. Operational semantics for hybrid systems. In Hybrid Systems: Computation and Control: 8th Internat. Workshop, pages 25-53, 2005.
15. J. Liu and E. A. Lee. A component-based approach to modeling and simulating mixed-signal and hybrid systems. ACM Transactions on Modeling and Computer Simulation, 12(4):343-368, 2002.
16. J. Liu, X. Liu, T. J. Koo, B. Sinopoli, S.Sastry, and E. A. Lee. A hierarchical hybrid system model and its simulation. In Proc. 38th IEEE Conference on Decision and Control, volume 4, pages 3508-3513, 1999.
17. J. Lygeros, K.H. Johansson, S.N. Simić, J. Zhang, and S. S. Sastry. Dynamical properties of hybrid automata. IEEE Trans. Aut. Cont., 48(1):2-17, 2003.
18. P.J. Mosterman and G. Biswas. A hybrid modeling and simulation methodology for dynamic physical systems. Simulation, 78:5-17, 2002.
19. R.T. Rockafellar and R. J-B Wets. Variational Analysis. Springer, 1998.
20. 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, pages 551-556, 2005.
21. R.G. Sanfelice, R. Goebel, and A.R. Teel. A feedback control motivation for generalized solutions to hybrid systems. In J. P. Hespanha and A. Tiwari, editors, Hybrid Systems: Computation and Control: 9th International Workshop, volume LNCS 3927, pages 522-536, 2006.
22. J. Sprinkle, A. D. Ames, A. Pinto, H. Zheng, and S. S. Sastry. On the partitioning of syntax and semantics for hybrid systems tools. In Proc. 44th IEEE Conference on Decision and Control and European Control Conference, 2005.
23. A. M. Stuart and A.R. Humphries. Dynamical Systems and Numerical Analysis. Cambridge University Press, 1996.
24. F.D. Torrisi and A. Bemporad. Hysdel - A tool for generating computational hybrid models for analysis and synthesis problems. IEEE Transactions on Control Systems Technology, 12:235-249, 2004.
25. A. van der Schaft and H. Schumacher. An Introduction to Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, Springer, 2000.