Stability and stabilization of two time scale switched systems in discrete time

IEEE Transactions on Automatic Control

Volumn 55, Issue 6, 2010, Pages 1434-1438

  Malloci, Ivan ^a   Daafouz, Jamal ^a   Iung, Claude ^a  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

Author keywords

Linear Matrix Inequalities; Lyapunov stability; Singular perturbation; Switched systems

Indexed keywords

ARBITRARY SWITCHING; DISCRETE TIME; LYAPUNOV STABILITY; NUMERICAL EXAMPLE; SINGULAR PERTURBATIONS; SLOW SUBSYSTEM; STABILITY PROPERTIES; SWITCHED LINEAR SYSTEM; SWITCHED QUADRATIC LYAPUNOV FUNCTION; SWITCHED SYSTEM; SWITCHED SYSTEMS; SWITCHING RULE; TECHNICAL NOTES; TWO TIME SCALE;

ASYMPTOTIC STABILITY; DIFFERENCE EQUATIONS; FEEDBACK; FEEDBACK CONTROL; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; STABILIZATION; STATE FEEDBACK; SWITCHING SYSTEMS; TIME MEASUREMENT;

SYSTEM STABILITY;

EID: 77953083751     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2044277     Document Type: Article

References (22)

1. D. S. Naidu, "Singular perturbations and time scales in control theory and applications: An overview," Dyn. Continuous, Discrete Impulsive Syst.. Series B. Appl. Algorith., vol.9, no.2, pp. 233-278, 2002.
2. P. Kokotovic, H. K. Khalil, and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design. New York: Academic Press, 1986.
3. P. Kokotovic and P. Sannuti, "Singular perturbation method for reducing the model order in optimal control design," IEEE Trans. Autom. Control, vol.AC-13, no.4, pp. 377-384, Aug. 1968.
4. B. D. O. Anderson, "Controller design: Moving from theory to practice," IEEE Control Syst. Mag., vol.13, no.4, pp. 16-25, 1993.
5. R. N. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King, "Stability criteria for switched and hybrid systems," SIAM Rev., vol.49, no.4, pp. 545-592, 2007. (Pubitemid 350263542)
6. H. Lin 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.
7. R. N. Shorten and K. S. Narendra, "Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems," Int. J. Adaptive Control Signal Processing, vol.16, no.10, pp. 709-728, 2002.
8. D. Liberzon, Switching in Systems and Control. Boston, MA: Birkhäuser, 2003.
9. S. Branicky, "Multiple Lyapunov function and other analysis tools for switched and hybrid systems," IEEE Trans. Autom. Control, vol.43, no.4, pp. 475-482, Apr. 1998.
10. J. Daafouz, P. Riedinger, and C. Iung, "Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach," IEEE Trans. Autom. Control, vol.47, no.11, pp. 1883-1887, Nov. 2002.
11. F. Blanchini, S. Miani, and C. Savorgnan, "Stability results for linear parameter varying and switching systems," Automatica, vol.43, no.10, pp. 1817-1823, 2007.
12. A. S. Morse, "Supervisory control of families of linear set-point controllers- Part 1: Exact matching," IEEE Trans. Autom. Control, vol.41, no.10, pp. 1413-1431, Oct. 1996.
13. J. Hespanha and A. S. Morse, "Stability of switched systems with average dwell-time," in Proc. IEEE Conf. Decision Control, 1999, pp. 2655-2660.
14. G. Zhai, B. Hu, K. Yasuda, and A. N. Michel, "Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach," Int. J. Syst. Sci., vol.32, no.8, pp. 1055-1061, 2001.
15. I. Malloci, J. Daafouz, C. Iung, R. Bonidal, and P. Szczepanski, "Switched system modeling and robust steering control of the tail end phase in a hot strip mill," Nonlin. Anal.: Hybrid Syst., vol.3, no.3, pp. 239-250, 2009.
16. M. Alwan, X. Liu, and B. Ingalls, "Exponential stability of singularly perturbed switched systems with time delay," Nonlin. Analy.: Hybrid Syst., vol.2, no.3, pp. 913-921, 2008.
17. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
18. I. Malloci, J. Daafouz, and C. Iung, "Stabilization of continuous-time singularly perturbed switched systems," in Proc. IEEE Conf. Decision Control, 2009, pp. 6371-6376.
19. B. Litkouhi and H. Khalil, "Multirate and composite control of twotime- scale discrete-time systems," IEEE Trans. Autom. Control, vol.AC-30, no.7, pp. 645-651, Jul. 1985.
20. V. D. Blondel and J. N. Tsitsiklis, "Complexity of stability and controllability of elementary hybrid systems," Automatica, vol.35, no.3, pp. 479-489, 1999.
21. P. Mason, M. Sigalotti, and J. Daafouz, "On stability analysis of linear discrete time switched systems using quadratic Lyapunov functions," in Proc. IEEE Conf. Decision Control, 2007, pp. 5629-5633. (Pubitemid 351278037)
22. B. S. Chen and C. L. Lin, "On the stability bounds of singularly perturbed systems," IEEE Trans. Autom. Control, vol.35, no.11, pp. 1265-1270, Nov. 1990.