Global Analysis of Piecewise Linear Systems Using Impact Maps and Surface Lyapunov Functions

IEEE Transactions on Automatic Control

Volumn 48, Issue 12, 2003, Pages 2089-2106

  Gonçalves, Jorge M ^a   Megretski, Alexandre ^b   Dahleh, Munther A ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Global stability; Hybrid systems; Impact and Poincar maps; Surface Lyapunov functions (SuLF)

Indexed keywords

ASYMPTOTIC STABILITY; GLOBAL OPTIMIZATION; LYAPUNOV METHODS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); STATE SPACE METHODS; SWITCHING;

GLOBAL STABILITY; HYBRID SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 9144246964     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.820061     Document Type: Article

References (20)

1. M. S. Branicky, "Studies in hybrid systems: modeling, analysis, and control," Ph.D. dissertation, Mass. Inst. Technol., Cambridge, MA, 1995.
2. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Trans. Automat. Contr., vol. 43, pp. 555-559, Apr. 1998.
3. J. M. Gonçalves, A. Megretski, and M. A. Dahleh, "Global stability of relay feedback systems," IEEE Trans. Automat. Contr., vol. 46, pp. 550-562, Apr. 2001.
4. G. Zames and P. L. Falb, "Stability conditions for systems with monotone and slope-restricted nonlinearities," in SIAM J. Control, vol. 6, 1968, pp. 89-108.
5. F. D'Amato, A. Megretski, U. Jönsson, and M. Rotea, "Integral quadratic constraints for monotonic and slope-restricted diagonal operators," in Proc. Amer. Control Conf., San Diego, CA, June 1999, pp. 2375-2379.
6. U. Jönsson and A. Megretski, "The Zames-Falb IQC for systems with integrators," IEEE Trans. Automat. Contr., vol. 45, pp. 560-565, Mar. 2000.
7. A. Megretski, "New IQC for quasiconcave nonlinearities," presented at the Amer. Control Conf., San Diego, CA, June 1999.
8. A. Megretski and A. Rantzer, "System analysis via integral quadratic constrains," IEEE Trans. Automat. Contr., vol. 42, pp. 819-830, June 1997.
9. 2-gain of double integrators with saturation nonlinearity," IEEE Trans. Automat. Contr., vol. 47, pp. 2063-2068, Dec. 2002.
10. _, "Constructive global analysis of hybrid systems," M.S. thesis, Mass. Inst. Technol., Cambridge, MA, Sept. 2000.
11. S. Pettersson and B. Lennartson, "An LMI approach for stability analysis of nonlinear systems," presented at the Eur. Control Conf., Brussels, Belgium, July 1997.
12. A. Hassibi and S. Boyd, "Quadratic stabilization and control of piecewise linear systems," presented at the Amer. Control Conf., Philadelphia, PA, 1998.
13. H. K. Khalil, Nonlinear Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1996.
14. P. A. Parrilo, "Structured Semidefinite Programs and semialgebraic geometry methods in robustness and optimization," Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2000.
15. Web Page. [Online]. Available: http://www.cds.caltech.edu/̃jmg/
16. A. Saberi, Z. Lin, and A. Teel, "Control of linear systems with saturating actuators," IEEE Trans. Automat. Contr., vol. 41, pp. 368-378, Mar. 1996.
17. H. J. Sussmann, E. D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls," IEEE Trans. Automat. Contr., vol. 39, pp. 2411-2425, Dec. 1994.
18. A. R. Teel, "A nonlinear small gain theorem for the analysis of control systems with saturation," IEEE Trans. Automat. Contr., vol. 41, pp. 1256-1270, Sept. 1996.
19. R. Suárez, J. Alvarez, and J. Alvarez, "Linear systems with single saturated input: Stability analysis," presented at the 30th Conf. Decision Control, Brighton, U.K., Dec. 1991.
20. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.