Computation of piecewise quadratic Lyapunov functions for hybrid systems

IEEE Transactions on Automatic Control

Volumn 43, Issue 4, 1998, Pages 555-559

  Johansson, Mikael ^a   Rantzer, Anders ^a  

^a LUND INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Linear matrix inequalities; Lyapunov stability; Piecewise linear systems

Indexed keywords

CALCULATIONS; CONTROL SYSTEMS; FUNCTIONS; OPTIMIZATION; SYSTEM STABILITY;

HYBRID SYSTEMS; POPOV CRITERIA;

LYAPUNOV METHODS;

EID: 0032045898     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.664157     Document Type: Article

References (18)

1. M. Corless, "Robust stability analysis and controller design with quadratic Lyapunov functions," in Variable Structure and Lyapunov Control, Lecture Notes in Control and Information Sciences, A. S. I. Zinober, Ed. New York: Springer, 1994, ch. 9, pp. 181-203.
2. F. Blanchini and S. Miani, "A new class of universal Lyapunov functions for the control of uncertain linear systems," in Proc. 35th Conf. Decision and Control, Kobe, Japan, Dec. 1996, pp. 1027-1032.
3. A. Rantzer and M. Johansson, "Piecewise linear quadratic optimal control," in Proc. American Control Conf., Albuquerque, NM, June 1997, to be published.
4. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," in Proc. European Control Conf., Brussels, Belgium, July 1997.
5. _, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," Dept. Automatic Control, Lund Inst. Tech., Lund, Sweden, Tech. Rep., June 1996.
6. S. Pettersson, "Modeling, control and stability analysis of hybrid systems," Licentiate thesis, Chalmers Univ., Nov. 1996.
7. M. Andersson, "Object-oriented modeling and simulation of hybrid systems," Ph.D. dissertation, Dept. Automatic Control, Lund Inst. Tech., Lund, Sweden, Dec. 1994.
8. J. Zhao, "System modeling, identification and control using fuzzy logic," Ph.D. dissertation, Université Catholique de Louvain, Belgium, 1995.
9. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox for Use with Matlab, The Mathworks Inc., May 1995.
10. L. El Ghaoui, LMITOOL: An Interface to Solve LMI Problems, ENSTA, 1995.
11. H. K. Khalil, Nonlinear Systems. New York: MacMillan, 1992.
12. M. A. Aiserman and F. R. Gantmacher, Die absolute Stabilität von Regel Systemen. Verlag, 1965, ch. II, p. 33.
13. V. A. Yakubovich, "S-procedure in nonlinear control theory," Vestnik Leningrad Univ., 1971, pp. 62-77,
14. V. A. Yakubovich, "S-procedure in nonlinear control theory," English translation in Vestnik Leningrad Univ., 1977, vol. 4, pp. 73-93.
15. M. S. Branicky, "Studies in hybrid systems: Modeling, analysis and control," Ph.D. dissertation, MIT, Cambridge, MA, 1995.
16. _, "Stability of switched hybrid systems," in Proc. 33rd Conf. Decision and Control, Lake Buena Vista, FL, Dec. 1994, pp. 3498-3503.
17. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides. Dordrecht, The Netherlands Kluwer, 1988.
18. V. I. Utkin, "Variable structure systems with sliding modes: A survey," IEEE Trans. Automat. Contr. vol. 22, pp. 212-222, 1977.