Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions

Applied Mathematics and Computation

Volumn 208, Issue 2, 2009, Pages 397-415

  Campbell, Stephen L ^a   Linh, Vu Hoang ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b VIETNAM NATIONAL UNIVERSITY   (Viet Nam)

Author keywords

Asymptotic stability; Delay differential algebraic equation; Multiple delays; Numerical solution; Regular pencil

Indexed keywords

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; NUMERICAL ANALYSIS; NUMERICAL METHODS; STABILITY;

BDF METHODS; COEFFICIENT MATRICES; DELAY DIFFERENTIAL-ALGEBRAIC EQUATION; DELAY INDEPENDENTS; DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH MULTIPLE DELAYS; MULTIPLE DELAYS; NUMERICAL SOLUTION; REGULAR PENCIL; STABILITY CONDITIONS; SUFFICIENT CONDITIONS;

STABILITY CRITERIA;

EID: 59149102070     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.12.008     Document Type: Article

References (26)

1. Ascher U., and Petzold L.R. Stability of computational methods for constrained dynamics systems. SIAM J. Sci. Comput. 14 1 (1993) 95-120
2. Ascher U., and Petzold L.R. The numerical solution of delay-differential-algebraic equations of retarded and neutral type. SIAM J. Numer. Anal. 32 (1995) 1635-1657
3. Brenan K.E., Campbell S.L., and Petzold L.R. Numerical Solution of Initial Value Problems in Differential Algebraic Equations (1996), SIAM, Philadelphia
4. Byers R., and Nichols N. On the stability radius of a generalized state-space system. Linear Algebra Appl. 188/189 (1993) 113-134
5. Campbell S.L. Singular linear systems of differential equations with delays. Appl. Anal. 11 (1980) 129-136
6. S.L. Campbell, 2-D (differential-delay) implicit systems, in: Proc. IMACS World Congress on Sci. Comp., Dublin, 1991, pp. 1828-1829.
7. Campbell S.L. Nonregular 2D descriptor delay systems. IMA J. Math. Cont. Inf. 12 (1995) 57-67
8. Cao Y., Li S., Petzold L.R., and Serban R. Adjoint sensitivity analysis for differential-algebraic equations: the adjoint DAE system and its numerical solution. SIAM J. Sci. Comput. 24 (2003) 1076-1089
9. Du N.H., and Linh V.H. Robust stability of implicit linear systems containing a small parameter in the leading term. IMA J. Math. Control Inform. 23 (2006) 67-84
10. Fridman E. Stability of linear descriptor systems with delay: a Lyapunov-based approach. J. Math. Anal. Appl. 273 (2002) 24-44
11. Griepentrog E., and März R. Differential-Algebraic Equations and their Numerical Treatment (1986), Teubner-Texte zur Mathematik, Leibzig
12. Hale J.K., and Verduyn Lunel S.M. Introduction to Functional Equations (1993), Springer-Verlag
13. Hu G.D., Hu G.D., and Cahlon B. Algebraic criteria for stability of linear neutral systems with a single delay. J. Comput. Appl. Math. 135 (2001) 125-133
14. He P., and Cao D.Q. Algebraic stability criteria of linear neutral systems with multiple time delays. Appl. Math. Comput. 155 (2004) 643-653
15. Kato T. Perturbation Theory for Linear Operators (1966), Springer-Verlag, New York, NY
16. Kunkel P., and Mehrmann V. Differential-Algebraic Equations. Analysis and Numerical Solution (2006), EMS Publishing House, Zürich, Switzerland
17. Lancaster P., and Tismenetsky M. The Theory of Matrices. second ed. (1985), Academic Press, Inc., Orlando, FL
18. Linh V.H. On the robustness of asymptotic stability for a class of singularly perturbed systems with multiple delays. Acta Math. Viet. 30 (2005) 137-151
19. Luzyanina T., and Roose D. Periodic solutions of differential algebraic equations with time-delays: computation and stability analysis. J. Bifurcation Chaos 16 (2006) 67-84
20. L. Poppe, The strangeness index of a linear delay differential-algebraic equation of retarded type, in: Proceedings of the Sixth IFAC Workshop on Time-Delay Systems, 2006, 5pp.
21. Qiu L., and Davison E.J. The stability robustness of generalized eigenvalues. IEEE Trans. Autom. Control 37 (1992) 886-891
22. Shampine L.F., and Gahinet P. Delay-differential-algebraic equations in control theory. Appl. Numer. Math. 56 (2006) 574-588
23. Stykel T. On criteria for asymptotic stability of differential-algebraic equations. Z. Angew. Math. Mech. 92 (2002) 147-158
24. Xu S., Van Dooren P., Radu S., and Lam J. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. Autom. Cont. 47 (2002) 1122-1128
25. Zhu W., and Petzold L.R. Asymptotic stability of linear delay differential-algebraic equations and numerical methods. Appl. Numer. Math. 24 (1997) 247-264
26. Zhu W., and Petzold L. Asymptotic stability of Hessenberg delay differential-algebraic equations of retarded or neutral type. Appl. Numer. Math. 27 (1998) 309-325