On linear passive complementarity systems

European Journal of Control

Volumn 8, Issue 3, 2002, Pages 220-237

  Camlibel M K ^a   Heemels, W P M H ^b   Schumacher, J M ^c  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c TILBURG UNIVERSITY   (Netherlands)

Author keywords

Hybrid systems; Linear complementarity problems and systems; Passivity; Piecewise linear systems; Stability; Switched networks

Indexed keywords

ASYMPTOTIC STABILITY; DIODES; MATHEMATICAL PROGRAMMING; NETWORKS (CIRCUITS);

HYBRID SYSTEMS; LINEAR COMPLEMENTARITY PROBLEMS AND SYSTEMS; PASSIVITY; PIECEWISE LINEAR SYSTEMS; SWITCHED NETWORKS;

LINEAR CONTROL SYSTEMS;

EID: 0038708651     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.8.220-237     Document Type: Article

References (34)

1. Alur R, Henzinger TA, Sontag ED (eds). Hybrid systems III. (Proceedings of the Workshop on Verification and Control of Hybrid Systems, New Brunswick, New Jersey, October 1995.), vol 1066 series lecture notes in Computer Science. Springer 1996
2. Anderson BDO, Vongpanitlerd S. Network analysis and synthesis: A modern systems theory approach. Prentice-Hall, Englewood Cliffs, New Jersey 1973
3. Branicky MS, Borkar VS, Mitter, SK. A unified framework for hybrid control: model and optimal control theory. IEEE Trans Autom Control 1998; 43(1): 31-45
4. Brogliato B. Absolute stability and the Lagrange-Dirichlet theorem with monotone multivalued mappings. 2000 (submitted)
5. Çamlibel MK. Complementarity methods in the analysis of pieccwise linear dynamical systems. PhD thesis, Tilburg University 2001
6. Çamlibel MK, Heemels WPMH, Schumacher JM. The nature of solutions to linear passive complementarity systems. In: CD-ROM Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix USA, 1999, pp 3043-3048
7. Çamlibel MK, Heemels WPMH, Schumacher JM. Well-posedness of a class of linear networks with ideal diodes. In: CD-ROM Proceedings of the 14th International Symposium of Mathematical Theory of Networks and Systems, Perpignan France, 2000
8. Cottle RW, Dantzig GB. Complementarity pivot theory of mathematical programming. In: Dantzig GB, Eaves BC (eds). Studies in optimization, vol 10 of MAA studies in mathematics. The Mathematical Association of America, 1974, pp 27-51
9. Cottle RW, Pang J-S, Stone RE. The linear complementarity problem. Academic Press, Boston 1992
10. DiStefano JJ, Stubberud AR, Williams IJ. Theory and problems of feedback and control systems. Schaum's outline series. McGraw-Hill 1967
11. Hautus MLJ, Silverman LM. System structure and singular control. Linear Algebra and its Appli 1983; 50: 369-402
12. Heemels WPMH, Çamlibel MK, Schumacher JM. On event driven simulation of electrical circuits with ideal diodes. Journal Européen des Systèmes Automatisés 2001; 35(4): 467-488
13. HeemelsWPMH, Çamlibel MK, Schumacher JM. On the dynamic analysis of piecewise linear networks, IEEE Transactions on Circuits and Systems-I, 2002; 49(3): 315-327
14. Heemels WPMH, Schumacher JM, Weiland S. The rational complementarity problem. Linear Algebra and its Appl 1999; 294(1-3): 93-135
15. Heemels WPMH, Schumacher JM, Weiland S. Linear complementarity systems. SIAM J Appl Math 2000; 60(4): 1234-1269
16. Khalil HK. Nonlinear systems. Prentice-Hall, Upper Saddle River, New Jersey 1996
17. Leenaerts DMW, van Bokhoven WMG. Piecesvise linear modelling and analysis. Kluwer Academic Publishers, Dordrecht, The Netherlands 1998
18. Lootsma YJ, van der Schaft AJ, Çamlibel MK. Uniqueness of solutions of relay systems. Automatica 1999; 35(3): 467-478
19. Luenberger DG, Linear and nonlinear programming. Addison-Wesley Publishing Company 1984
20. Lütkepohl H. Handbook of matrices. Wiley, New York 1996
21. Lygeros J, Johansson KH, Sastry S, Egerstedt M. On the existence and uniqueness of executions of hybrid automata. In: 38-th IEEE Conference on Decision and Control, Phoenix USA, 1999, pp 2249-2254
22. Lynch N, Segala R, Vaandrager F, Weinberg HB. Hybrid I/O automata. In [1] pp 496-510, 1996
23. Mangasarian OL. Nonlinear programming. McGraw-Hill, New York 1969
24. Monteiro Marques MDP. Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction. Progress in Nonlinear Differential Equations and their Applications. Birkhäuser, Basel 1993
25. Popov VM. Hyperstability and optimality of automatic systems with several control functions. Revue Roumaine Sci Tech Electrotech et Energ 1964; 9: 629-690
26. Popov VM. Hyperstability of control systems. Springer-Verlag, New York 1973.
27. Richards JI, Youn HK. Theory of Distributions: A Non-technical Introduction. Cambridge Uni. Press, Cambridge 1990
28. Rudin W. Principles of mathematical analysis. McGraw-Hill, New York 1976
29. van der Schaft AJ, Schumacher JM. The complementary-slackness class of hybrid systems. Math Control, Signal Syst 1996; 9: 266-301
30. van der Schaft AJ, Schumacher JM. Complementarity Modelling of hybrid systems. IEEE Trans Autom Control 1998; 43(4): 483-490
31. van der Schaft AJ, Schumacher JM. An introduction to hybrid dynamical systems, vol 251 of lecture notes in control and liformation sciences. Springer, London 1999
32. Stoer J, Witzgall C. Convexity and optimization in Finite dimensions I. Springer, Berlin 1970
33. Vidyasagar M. Nonlinear systems analysis. Prentice-Hall, Englewood Cliffs, New Jersey 1993
34. Willems JC. Dissipative dynamical systems. Arch Ration Mech Anal 1972; 45: 321-393