Aspects of Modeling Dynamical Systems by Differential-Algebraic Equations

Mathematical and Computer Modelling of Dynamical Systems

Volumn 7, Issue 2, 2001, Pages 133-143

  Muller P C ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

Descriptor systems; Differential algebraic equations; Singular control systems

Indexed keywords

EID: 0035561954     PISSN: 13873954     EISSN: None     Source Type: Journal    
DOI: 10.1076/mcmd.7.2.133.3650     Document Type: Article

References (45)

1. Arnold, M.: Zur Theorie und zur numerischen Lösung von Anfangswertproblemen für differentiell-algebraische Systeme von höherem Index. Fortschr.-Ber. VDI, Reihe 20, Nr. 264, VDI-Verlag, Düsseldorf, 1998.
2. Bajic, V.: Lyapunov's Direct Method in the Analysis of Singular Systems and Networks. Shades Technical Publications, Hiicrest, RSA, 1992.
3. Brenan, K.E., Campbell, S.L. and Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. North-Holland, New York, 1989.
4. Bunse-Gerstner, A., Mehrmann, V. and Varga, A.: Numerische Methoden zur robusten Steuerung. DFG-Forschungsprojekt. Zentrum fur Technomathematik, Universitat Bremen, Tatigkeitsbericht 1999/2000.
5. Campbell S.L., Nikoukhah, R. and Delebecque, F.: Nonlinear Descriptor Systems. In: P.M. Frank (ed.): Advances in Control-Highlights of ECC '99, Springer, London, 1999, pp. 247-281.
6. Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer, Berlin-Heidelberg, 118 (1989).
7. Eich, E., Burr, P., Kröner, A. and Lory, P.: Modellierung und numerische Simulation in der chemischen Verfahrenstechnik. In: A. Bachem, M. Jürgens and R. Schrader (eds.): Mathematik in der Praxix. Springer, Berlin-Heidelberg, 1995, pp. 61-85.
8. Führer, C.: Differential-algebraische Gleichungssysteme in mechanischen Mehrkörpersystemen: Theorie, numerische Ansätze und Anwendungen. Dissertation, Mathematisches Institut und Institut für Informatik. TU München, 1988.
9. Fürst, D.: Mathematische Modellbildung, regelungstechnische Analyse und Synthese mechatronischer Systeme in Deskriptorform. Shaker, Aachen, 2000.
10. Gear, C.W.: The Simultaneous Numerical Solution of Differential-Algebraic Equations. IEEE Trans. Circuit Theory 18 (1971), pp. 89-95.
11. Hairer, E. and Wanner, G.: Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems. Springer, Berlin-Heidelberg, 1991.
12. Kampowsky, W., Rentrop, P. and Schmidt, W.: Classification and Numerical Simulation of Electric Circuits. Surveys on Mathematics for Industry 2 (1992), pp. 23-65.
13. Kröner, A., Holl, P., Marquardt, W. and Gilles, E.D.: DIVA - An Open Architecture for Dynamic Simulation. Comp. Chem. Eng. 14 (1990), pp. 1289-1295.
14. Kumar, A. and Daoutidas, P.: Feedback Control of Nonlinear Differential-Algebraic-Equation Systems. AIChE Journal 41 (1995), pp. 619-636.
15. ∞-Problem for Descriptor Systems. In: Y. Yamamoto and S. Hara (eds.): Learning, Control and Hybrid Systems. Springer, London, 1999.
16. Lewis, F.L.: A Survey of Linear Singular Systems. Circuits, Systems and Signal Processing, 5 (1986), pp. 3-36.
17. Lubich, Ch., Engstler, Ch., Nowak, U. and Pöhle, U.: Numerical integration of constrained mechanical systems using MEXX. Mechanics of Structures and Machines 23 (1995), pp. 473-495.
18. Luenberger, D.G.: Dynamic Equations in Descriptor Form. IEEE Trans. Automatic Control 22 (1977), pp. 312-321.
19. ∞-Control for Descriptor Systems: A Matrix Inequalities Approach. Automatica 33 (1997), pp. 669-673.
20. Mathis, W.: Analysis of Linear Time-Invariant Networks in the Frequency Domain. In: R.E. Bank, R. Bulirsch, H. Gajewski and K. Merterns (eds.): Mathematical Modeling and Simulation of Electrical Circuits and Semiconductor Devices. Birkhäuser, Basel, 1992, pp. 83-90.
21. Müller, P.C.: Stability of Linear Mechanical Systems with Holonomic Constraints. Applied Mechanics Review 46 (1993), No. 11, Part 2, pp. S160-S164.
22. Müller, P.C.: Descriptor Systems: A New Way to Model Mechatronic System? In: Proc. 3rd European Control Conference. Rome, 1995, Vol. 3, Part 2, pp. 2725-2729.
23. Müller, P.C.: Stability of Nonlinear Descriptor Systems. Z. Angew. Math. Mech. 76 (1996), Supplement 4, pp. 9-12.
24. Müller, P.C.: Stability and Optimal Control of Nonlinear Descriptor Systems: A Survey. Appl. Math. and Comp. Sci., 8 (1998), pp. 269-286.
25. Müller, P.C.: 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.
26. Müller, P.C.: Linear Control Design of Linear Descriptor Systems. In: Proc. 14th IFAC World Congress, Beijing, 1999, Pergamon, 1999, Vol. C, pp. 31-36.
27. Müller, P.C.: Verallgemeinerte Luenberger-Beobachter für lineare Deskriptorsysteme. Z. Angew. Math. Mech., 79 (1999), Supplement 1, pp. S9-S12.
28. Müller, P.C.: Descriptor Systems: Pros and Cons of System Modeling by Differential-Algebraic Equations. In: I. Troch and F. Breitenecker (Eds.): Proc. 3rd IMACS Symposium on Mathematical Modelling, ARGESIM Report 15, Vol. 1, pp. 231-235, Wien 2000. Revised version in: Math. Comp. Simul. 53 (2000), pp. 273-279.
29. Müller, P.C.: Descriptor Systems: Pros and Cons of System Modeling by Differential-Algebraic Equations. In: I. Troch and F. Breitenecker (Eds.): Proc. 3rd IMACS Symposium on Mathematical Modelling, ARGESIM Report 15, Vol. 1, pp. 231-235, Wien 2000. Revised version in: Math. Comp. Simul. 53 (2000), pp. 273-279.
30. Müller, P.C.: Linear-Quadratic Optimal Control of Non-Proper Descriptor Systems. CD-Proc. 14th Internat. Symp. Mathematical Theory of Networks and Systems (MTNS 2000), Universite de Perpignan, 2000.
31. Müller, Pia: Linearisierung und Entkopplung von Deskriptorsystemen. Shaker, Aachen, 2000.
32. Panreck, K., Jahnich, M. and Dörrscheidt, F.: Verwendung differential-algebraischer Gleichungen zur verkopplungsorientierten Modellierung komplexer Prozesse. Automatisierungstechnik 42 (1994), pp. 239-247.
33. Petzold, L.R.: 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.
34. Rehm, A. and Allgöwer, F.: Control of Descriptor Systems with High Index. Proc. 14th IFAC World Congress, Beijing, D (1999), pp. 31-37.
35. Rosenberg, R.M.: Analytical Dynamics of Discrete Systems. Plenum Press, New York 1977.
36. Rükgauer, A. and Schiehlen, W.: Simulation of Modular Dynamic Systems. In: Proc. 2nd MATHMOD. Vienna, 1997, pp. 329-334.
37. Rükgauer, A.: Modulare Simulation mechatronischer Systeme mit Anwendung in der Fahrzeugdynamik. VDI-Fortschr.-Ber., Reihe 20, Nr. 248, VDI, Düsseldorf, 1997.
38. Schiehlen, W.: Multibody Systems Handbook. Springer, Berlin-Heidelberg, 1990.
39. Simeon, B.: Numerische Integration mechanischer Mehrkörpersysteme: Projizierende Deskriptorformen, Algorithmen und Rechenprogramme. VDI-Fortschr.-Ber., Reihe 20, Nr. 130, VDI, Düsseldorf, 1994.
40. Simeon, B: MBSPACK - Numerical integration software for constrained mechanical motion. Survey on Mathematics for Industry 5 (1995), pp. 169-202.
41. ∞-Control for Descriptor Systems - A J-Spectral Factorization Approach. In: Proc. 33rd IEEE Conf. Decision and Control, 1994, pp. 2251-2256.
42. Van Dooren, P.: The Generalized Eigenstructure Problem in Linear System Theory. IEEE Trans. Automatic Control 26 (1981), pp. 111-129.
43. Varga, A.: Descriptor System Toolbox for MATLAB. Institute of Robotic and Mechatronics, German Aerospace Center, Oberpfaffenhofen, 2000.
44. Weiss, M. and Preisig, H.A.: Structural Analysis in the Dynamical Modelling of Chemical Engineering Systems. Math. Comp. Modeling Dynam. Systems 6 (2000), pp. 325-364.
45. Xing, W., Zhang, Q. and Wang, Q: State-Feedback Control Based on Observer for Descriptor System. Proc. 3rd Asian Control Conference, Shanghai 2000, pp. 1259-1263.