Descriptor systems: Pros and cons of system modelling by differential-algebraic equations

Mathematics and Computers in Simulation

Volumn 53, Issue 4-6, 2000, Pages 273-279

  Muller P C ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

Descriptor systems; Differential algebraic equations

Indexed keywords

EID: 17544395289     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(00)00213-5     Document Type: Article

References (30)

1. V. Bajic, Lyapunov's Direct Method in the Analysis of Singular Systems and Networks, Shades Technical Publications, Hiicrest, RSA, 1992.
2. K.E. Brenan, S.L. Campbell, L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
3. L. Dai, Singular control systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer, Berlin, 1989.
4. E. Eich, P. Burr, A. Kröner, P. Lory, Modellierung und numerische Simulation in der chemischen Verfahrenstechnik, in: A. Bachem, M. Jürgens, R. Schrader (Eds.), Mathematik in der Praxis, Springer, Berlin, 1995, pp. 61-85.
5. C.W. Gear, The simultaneous numerical solution of differential-algebraic equations, IEEE Trans. Circuit Theory 18 (1971) 89-95.
6. E. Hairer, G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer, Berlin, 1991.
7. W. Kampowsky, P. Rentrop, W. Schmidt, Classification and numerical simulation of electric circuits, Surv. Math. Ind. 2 (1992) 23-65.
8. A. Kumar, P. Daoutidas, Feedback control of nonlinear differential-algebraic-equation systems, AIChE J. 41 (1995) 619-636.
9. ∞-problem for descriptor systems, in: Y. Yamamoto, S. Hara (Eds.), Learning, Control and Hybrid Systems, Springer, London, 1999.
10. F.L. Lewis, A survey of linear singular systems, Circuits, Syst. Signal Processing 5 (1986) 3-36.
11. D.G. Luenberger, Dynamic equations in descriptor form, IEEE Trans. Automatic Control 22 (1977) 312-321.
12. ∞-control for descriptor systems: a matrix inequalities approach, Automatica 33 (1997) 669-673.
13. W. Mathis, Analysis of linear time-invariant networks in the frequency domain, in: R.E. Bank, R. Bulirsch, H. Gajewski, K. Mertens (Eds.), Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices, Birkhäuser, Basel, 1992, pp. 83-90.
14. P.C. Müller, Stability of linear mechanical systems with holonomic constraints, Appl. Mech. Rev. 46 (11) Part 2 (1993) S160-S164.
15. P.C. Müller, Descriptor systems: a new way to model mechatronic system?, in: Proceedings of the 3rd European Control Conference, Vol. 3, Part 2, Rome, 1995, pp. 2725-2729.
16. P.C. Müller, Stability of nonlinear descriptor systems, Z. Angew. Math. Mech. 76 (Suppl. 4) (1996) 9-12.
17. P.C. Müller, Stability and optimal control of nonlinear descriptor systems: a survey, Appl. Math. Comp. Sci. 8 (1998) 269-286.
18. P.C. Müller, Analysis and control design of linear descriptor systems, in: V. Bajic (Ed.), Advances in Systems, Signals, Control and Computers, Vol. I, Center for Engineering Research, Technikon Natal, Durban, RSA, 1998, pp. 11-17.
19. P.C. Müller, Linear control design of linear descriptor systems, in: Proceedings of the 14th IFAC World Congress, Beijing, 1999, Vol. C, Pergamon, 1999, pp. 31-36.
20. P.C. Müller, Verallgemeinerte Luenberger-Beobachter für lineare Deskriptorsysteme, Z. Angew. Math. Mech. 79 (Suppl. 1) (1999) S9-S12.
21. K. Panreck, M. Jahnich, F. Dörrscheidt, Verwendung differential-algebraischer Gleichungen zur verkopplungsorientierten Modellierung komplexer Prozesse, Automatisierungstechnik 42 (1994) 239-247.
22. L.R. Petzold, A description of DASSL: a differential/algebraic system solver, in: R.S. Stepleman et al. (Eds.), Scientific Computing, North-Holland, Amsterdam, 1983, pp. 65-68.
23. ∞-control of descriptor systems with high index, Proc. IFAC 14th World Congress, Pergamon Publ. 1999, Vol. 0, pp. 31-37.
24. R.M. Rosenberg, Analytical Dynamics of Discrete Systems, Plenum Press, New York, 1977.
25. A. Rükgauer, W. Schiehlen, Simulation of modular dynamic systems, in: Proceedings of the 2nd MATHMOD, Vienna, 1997, pp. 329-334.
26. A. Rükgauer, Modulare Simulation mechatronischer Systeme mit Anwendung in der Fahrzeugdynamik, Reihe 20, Nr. 248, VDI-Fortschr.-Ber. VDI, Düsseldorf, 1997.
27. W. Schiehlen, Multibody Systems Handbook, Springer, Berlin, 1990.
28. B. Simeon, Numerische Integration mechanischer Mehrkörpersysteme: Projizierende Deskriptorformen, Algorithmen und Rechenprogramme, Reihe 20, Nr. 130, VDI-Fortschr-Ber. VDI, Düsseldorf, 1994.
29. ∞-control for descriptor systems - a J-spectral factorization approach, in: Proceedings of the 33rd IEEE Conference Decision and Control, 1994, pp. 2251-2256.
30. P. Van Dooren, The generalized eigenstructure problem in linear system theory, IEEE Trans. Automatic Control 26 (1981) 111-129.