On inconsistent initial conditions for linear time-invariant differential-algebraic equations

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 49, Issue 11, 2002, Pages 1646-1647

  Reißig, Gunther ^a   Boche, Holger ^b   Barton, Paul I ^a  

^a Massachusetts Institute of Technology   (United States)

^b Broadband Mobile Commun Networks   (Germany)

Author keywords

Differential algebraic equations (DAEs)

Indexed keywords

ALGEBRA; LAPLACE TRANSFORMS; LINEAR EQUATIONS; LINEAR SYSTEMS;

DERIVATION; DIFFERENTIAL ALGEBRAIC EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0036861697     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2002.804552     Document Type: Article

References (26)

1. P. I. Barton and C. K. Lee, "Modeling, simulation, sensitivity analysis and optimization of hybrid systems," Dept. Chem. Eng, MIT, Cambridge, MA, Tech. Rep., Sept. 2001.
2. P. I. Barton and S. Galán, "Linear DAEs with nonsmooth forcing," Dept. Chem. Eng, Massachusetts Inst. Technol., Cambridge, MA, Tech, Rep., Jan. 26, 2000.
3. D. Bedrosian and J. Vlach, "Time-domain analysis of networks with internally controlled switches," IEEE Trans. Circuits Syst. I, vol. 39, pp. 199-212, Mar. 1992.
4. K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Philadelphia, PA: SIAM, 1996.
5. L, Brüll and U. Pallaske, "On DAEs with discontinuities," Z. Angew. Math. Phys., vol. 43, no. 2, pp. 319-327, 1992.
6. S. L. Campbell, "Singular systems of differential equations," Res. N. Math., vol. 40, 1980.
7. D. Cobb, "On the solutions of linear differential equations with singular coefficients," J. Differ. Equ., vol. 46, no. 3, pp. 310-323, 1982.
8. G. Doetsch, Handbuch der Laplace-Transformation. Bd II. Anwendungen der Laplace-Transformation. 1. Abteilung. Basel. Germany: Birkhäuser Verlag, 1955.
9. ____, Einführung in Theorie and Anwendung der Laplace-Transformation, 2 ed. Berlin, Germany: Birkhäuser, 1970.
10. V. Doležal, Dynamics of Linear Systems. Prague, Czech Republic: Academia, 1967.
11. E. Fubini Ghiron, "Sopra alcuni procedimenti di calcolo operazionale," Rend. Circ. Mat. Palermo, vol. 61, pp. 1-42, 1937.
12. F. R. Gantmacher, Matrizentheorie (The Theory of matrices, Chelsea, New York, 1959). Berlin, Germany: VEB Dt. Verl. d. Wiss., 1986.
13. A. Ghizzetti, "Sull'uso della transformazione di Laplace nello studio dei circuiti elettrici," Rend. Circ. Mat. Palermo, vol. 61, pp. 339-368, 1937.
14. V. Gopal and L. T. Biegler, "A successive linear programming approach for initialization and reinitialization after discontinuities of differential-algebraic equations," SIAM J. Sci. Comput.,vol. 20, no. 2, pp. 447-467, 1999.
15. W. Q. Liu, W.Y. Yan, and K. L. Teo, "On initial instantaneous jumps of singular systems," IEEE Trans. Automat. Control, vol. 40, pp. 1650-1655, Sept. 1995.
16. C. Majer, W. Marquardt, and E. D. Gilles, "Reinitialization of DAE's after discontinuities," Comput. Chem. Eng., vol. 19 (Suppl.), pp. S507-S512, 1995.
17. E. Mohr, "Integration von gewöhnlichen differentialgleichungen mit konstanten koeffizienten mittels operatorenrechnung," Math. Nachr., vol. 10, pp. 1-49, 1953.
18. L. Petzold, "Differential/algebraic equations are not ODE's," SIAM J. Sci. Stat. Comput., vol. 3, no. 3, pp. 367-384, 1982.
19. P.J. Rabier and W. C. Rheinboldt, "Classical and generalized solutions of time-dependent linear differential-algebraic equations," Linear Algebra Appl., vol. 245, pp. 259-293, 1996.
20. ____, "Discontinuous solutions of semilinear differential-algebraic equations-Parts I, II," Nonlinear Anal., vol.27, no. 11, pp. 1241-1256, 1257-1280, 1996.
21. ____ "Time-dependent linear DAEs with discontinuous inputs," Linear Algebra Appl., vol. 247, pp. 1-29, 1996.
22. G. Reißig, "Differential-algebraic equations and impasse points," IEEE Trans. Circuits Syst. I, vol. 43, pp. 122-133, Feb. 1996.
23. G. Reißig, W. S. Martinson, and P. I. Barton, "Differential-algebraic equations of index 1 may have an arbitrarily high structural index," SIAM J. Sci. Comput., vol. 21, no. 6, pp. 1987-1990, 2000.
24. S. Seshu and N. Balabanian, Linear Network Analysis. New York: Wiley, 1959.
25. R. F. Sincovec, A. M. Erisman, E. L. Yip, and M. A. Epton, "Analysis of descriptor systems using numerical algorithms," IEEE Trans. Automat. Contr., vol. 26, pp. 139-147, Jan. 1981.
26. Z. Zuhao, "ZZ model method for initial condition analysis of dynamics networks," IEEE Trans. Circuits Syst., vol. 38, pp. 937-941, Aug. 1991.