Structural stability of boundary equilibria in a class of hybrid systems: Analysis and use for control system design

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 215-220

  Bernardo, Mario Di ^a,b   Camlibel, Kanat ^c,d  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^d DOGUS UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR CONTROL SYSTEMS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; PHASE SPACE METHODS; SWITCHING SYSTEMS; SYSTEM STABILITY;

BOUNDARY EQUILIBRIA; HYBRID SYSTEMS; STRUCTURAL STABILITY;

CONTROL SYSTEM ANALYSIS;

EID: 33847213209     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582157     Document Type: Conference Paper

References (23)

1. B. Brogliato, Nonsmooth Mechanics. Springer-Verlag, 1999.
2. S. Banerjee and G. Verghese, Nonlinear Phenomena in Power Electronics. IEEE Press, 2001.
3. M. di Bernardo, F. Garofalo, L. Glielmo, and F. Vasca, "Switchings, bifurcations and chaos in dc/dc converters," IEEE Trans. on Circuits and Systems I, vol. 45, no. 2, pp. 133-143, 1998.
4. J. Keener and J. Sneyd, Mathematical Physiology. Springer-Verlag, 1998.
5. C. S. Daw, M. B. Kennel, C. E. A. Finney, and F. T. Connolly, "Observing and modeling nonlinear dynamics in an internal combustion engine," Physical Review E, vol. 57, no. 3, pp. 2811-2819, 1998.
6. M. Garcia, A. Chatterjee, A. Ruina, and M. Coleman, "The simplest walking model: stability, complexity and scaling," ASME Journal of Biomechanical Engineering, 1998.
7. V. I. Utkin, Sliding Modes in Control Optimization. Springer-Verlag, 1992.
8. Ya. Z. Tsypkin, Relay Control Systems. Cambridge, U.K.: Cambridge University Press, 1984.
9. J. G. Kassakian, M. F. Schlecht, and G. C. Verghese, Principles of Power Electronics. Addison-Wesley, 1991.
10. J. Guckenheimer, "A robust hybrid stabilization strategy for equilibria," IEEE Transactions on Automatic Control, vol. 40, no. 2, pp. 321-326, 1995.
11. M. di Bernardo and F. Vasca, "On discrete time maps for the analysis of bifurcations and chaos in dc/dc converters," IEEE Trans. on Circuits and Systems I, vol. 47, no. 2, pp. 130-143, 2000.
12. P. Kowalczyk and M. di Bernardo, "On a novel class of bifurcations in hybrid dynamical systems: the case of relay feedback systems," Proceedings Hybrid Systems: Computation and Control Conference (HSCC01), pp. 361-374, 2001.
13. M. di Bernardo, K. H. Johansson, and F. Vasca, "Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations," International Journal of Bifurcation and Chaos, vol. 11, pp. 1121-1140, 2001.
14. M. di Bernardo, C. J. Budd, and A. R. Champneys, "Unified framework for the analysis of grazing and border-collisions in piecewise-smooth systems," Physical Review Letters, vol. 86, no. 12, pp. 2554-2556, 2001.
15. M. di Bernardo, M. I. Feigin, S. J. Hogan, and M. E. Homer, "Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems," Chaos, Solitons and Fractals, vol. 10, pp. 1881-1908, 1999.
16. M. di Bernardo, C. J. Budd, and A. R. Champneys, "Normal form maps of grazing bifurcations in n-dimensional piecewise-smooth systems," 2001, to appear on Physica D.
17. _, "Corner-collision implies border-collision bifurcation," Physica D, vol. 154, pp. 171-194, 2001.
18. E. Freire, E. Ponce, F. Rodrigo, and F. Torres, "Bifurcation sets of continuous piecewise linear systems with two zones," International Journal of Bifurcation and Chaos, vol. 8, no. 11, pp. 2073-2097, 1998.
19. R. T. Leine, D. H. van Campen, and B. L. van de Vrande, "Bifurcations in nonlinear discontinuous systems," Nonlinear Dynamics, vol. 23, no. 2, pp. 105-164, 2000.
20. V. Blondel and J. Tsitsiklis, "Complexity of stability and controllability of elementary hybrid systems," Automatica, vol. 35, no. 3, pp. 479-490, 1999.
21. M. Camlibel, W. Heemels, and J. Schumacher, "Stability and controllability of planar bimodal complementarity systems," in Proceedings IEEE Conference on Decision ana Control, 2003.
22. G. Olivar, M. di Bernardo, and F. Angulo, "Hopf-like transitions in nonsmooth dynamical systems: the case of dc/dc converters," Proceeding IEEE ISCAS (International Symposium on Circuits and Systems, vol. 1, 2004.
23. V. Carmona, E. Freire, E. Ponce, and F. Torres, "Bifurcation of invariant cones in piecewise linear homogeneous systems," 2004, preprint.