Discrete-time modeling and stability analysis of periodic orbits with sliding for switched linear systems

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 57, Issue 11, 2010, Pages 2948-2955

  Zhao, Yibo ^a   Feng, Jiuchao ^a   Tse, Chi K ^b  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Discrete time mapping; sliding; stability; switched linear systems (SLSs)

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; LINEAR SYSTEMS; MAPPING; RELAY CONTROL SYSTEMS;

ANALYSIS AND SIMULATION; DISCRETE TIME; DISCRETE-TIME MODEL; DYNAMICAL EQUATION; OSCILLATING CIRCUITS; RELAY FEEDBACK SYSTEMS; SLIDING; SWITCHED LINEAR SYSTEM;

SYSTEM STABILITY;

EID: 78149464532     PISSN: 15498328     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2010.2050230     Document Type: Article

References (32)

1. P. G. Otanez and M. E. Campbell, "Bounded switched linear estimator for smooth nonlinear systems", IEEE Trans. Control Syst. Technol., vol. 15, no. 2, pp. 358-368, Mar. 2007.
2. L. Hai and P. J. Antsaklis, "Stability and stabilizability of switched linear systems: A survey of recent results", IEEE Trans. Autom. Control, vol. 54, no. 2, pp. 308-322, Feb. 2009.
3. C. K. Tse, "Flip bifurcation and chaos in three-state boost switching regulators", IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 41, no. 1, pp. 16-23, Jan. 1994.
4. S. Banerjee, S. Parui, and A. Gupta, "Dynamical effects of missed switching in current-mode controlled DC-DC converters", IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 51, no. 12, pp. 649-654, Dec. 2004.
5. M. di Bernardo, F. Garefalo, L. Glielmo, and F. Vasca, "Switchings, bifurcations, and chaos in DC/DC converters", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 2, pp. 133-141, Feb. 1998.
6. L. O. Chua and G. N. Lin, "Canonical realization of Chua's circuit family", IEEE Trans. Circuits Syst., vol. 37, no. 7, pp. 885-902, Jul. 1990.
7. M. M. Williamson, "Robot arm control exploiting natural dynamics", Ph. D. dissertation, MIT, Cambridge, MA, Jun. 1999.
8. C. R. Cahn, "Piecewise linear analysis of phase-lock loops", IEEE Trans. Space Electron. Telemetry, vol. 8, no. 1, pp. 8-13, Mar. 1962.
9. K. Tadashi and S. Masanori, "Chaotic and periodic motions in a vibroimpacting system", Int. J. Mech. Syst. Mach. Elements Manuf., vol. 46, no. 2, pp. 659-665, Jun. 2003.
10. M. di Bernardo, K. H. Johansson, and F. Vasca, "Self-oscillations in relay feedback systems: Symmetry and bifurcations", Int. J. Bifurc. Chaos, vol. 11, no. 4, pp. 1121-1140, Apr. 2001.
11. S. Banerjee, P. Ranjan, and C. Grebogi, "Bifurcations in two-dimensional piecewise smooth maps-theory and applications in switching circuits", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 5, pp. 633-643, May 2000.
12. G. M. Maggio, M. di Bernardo, and M. P. Kennedy, "Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 8, pp. 1160-1177, Aug. 2000.
13. Z. T. Zhusubaliyev and E. Mosekilde, "Torus birth bifurcations in a DC/DC converter", IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 8, pp. 1839-1850, Aug. 2006.
14. M. di Bernardo, P. Kowalczyk, and A. Nordmark, "Bifurcations of dynamical systems with sliding: Derivation of normal-form mappings", Phys. D, vol. 170, no. 3/4, pp. 175-205, Sep. 2002.
15. A. Colombo, "Boundary intersection crossing bifurcation in the presence of sliding", Phys. D, vol. 237, no. 22, pp. 2900-2912, Nov. 2008.
16. P. Kowalczyka and P. T. Piiroinenb, "Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator", Phys. D, vol. 237, no. 8, pp. 1053-1073, Jun. 2008.
17. P. Kowalczyk and M. di Bernardo, "Two-parameter degenerate sliding bifurcations in Filippov systems", Phys. D, vol. 204, no. 3/4, pp. 204-229, May 2005.
18. M. di Bernardo, A. R. Champneys, C. J. Budds, and F. Vasca, "Sliding orbits and double spiral bifurcation diagrams in power electronic dc/dc converters", in Proc. IEEE Int. Symp. Circuits Syst., 1999, pp. 262-265.
19. R. Tymerski, "Volterra series modeling of power conversion systems", IEEE Trans. Power Electron., vol. 6, no. 4, pp. 712-718, Oct. 1991.
20. B. Michele, "Harmonic balance, Melnikov method and nonlinear oscillators under resonant perturbation", Int. J. Circuits Theory Appl., vol. 36, no. 3, pp. 247-274, May 2008.
21. R. Genesio and G. Bagni, "A view on limit cycle bifurcations in relay feedback systems", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 8, pp. 1134-1140, Aug. 2003.
22. L. O. Chua and T. Yaw-Shing, "Nonlinear oscillation via Volterra series", IEEE Trans. Circuits Syst., vol. CAS-29, no. 3, pp. 150-168, Mar. 1982.
23. V. Lanza, M. Bonnin, and M. Gilli, "On the application of the describing function technique to the bifurcation analysis of nonlinear systems", IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 4, pp. 343-347, Apr. 2007.
24. H. K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice-Hall, 2002.
25. K. H. Johansson, A. E. Barabanov, and K. J. Åström, "Limit cycles with chattering in relay feedback systems", IEEE Trans. Autom. Control, vol. 47, no. 9, pp. 1414-1423, Sep. 2002.
26. F. Dercole, A. Gragnani, Y. A. Kuznetsov, and S. Rinaldi, "Numerical sliding bifurcation analysis: An application to a relay control system", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 8, pp. 1058-1063, Aug. 2003.
27. F. B. Cunha, D. J. Pagano, and U. F. Moreno, "Sliding bifurcations of equilibria in planar variable structure systems", IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 8, pp. 1129-1134, Aug. 2003.
28. V. I. Utkin, Sliding Modes in Control Optimization. New York: Springer-Verlag, 1992.
29. J. Gonçalves, "Regions of stability for limit cycle oscillations in piecewise linear systems", IEEE Trans. Autom. Control, vol. 50, no. 11, pp. 1877-1882, Nov. 2005.
30. Y. Zhao, J. Feng, and C. K. Tse, "Stability analysis of periodic orbits non-autonomous piecewise-linear systems by mapping approach", IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 56, no. 11, pp. 845-849, Nov. 2009.
31. T. Kousaka, T. Ueta, and H. Kawakami, "Bifurcation of nonlinear dynamical systems", IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 46, no. 2, pp. 878-885, Jul. 1990.
32. H. Kawakami and R. Lozi, "Switched dynamical systems-Dynamical of a class of circuits with switch-structure and bifurcations of dynamical systems", in Proc. RIMS Conf., S. Ushiki, Ed., 1992, pp. 39-58.