Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback

Dynamical Systems

Volumn 26, Issue 1, 2011, Pages 85-101

  Kiss, Gábor ^a,b   Krauskopf, Bernd ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF SZEGED   (Hungary)

Author keywords

delay differential equations; distributed delay; hybrid testing

Indexed keywords

DELAY DIFFERENTIAL EQUATIONS; DELAY DISTRIBUTIONS; DELAY EQUATIONS; DELAY SYSTEMS; DISTRIBUTED DELAYS; HYBRID TESTING; MATHEMATICAL MODELLING; MEAN DELAYS; SECOND ORDERS; SECOND-ORDER DELAY EQUATIONS; SECOND-ORDER SYSTEMSS; STABILITY CHART; STABILIZING EFFECTS; TWO EQUATION; ZERO SOLUTIONS;

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; TIME DELAY; STABILITY;

DISTRIBUTION FUNCTIONS;

EID: 79951816267     PISSN: 14689367     EISSN: 14689375     Source Type: Journal    
DOI: 10.1080/14689367.2010.523889     Document Type: Article

References (18)

1. S.A. Campbell and R. Jessop, Approximating the stability region for a differential equation with a distributed delay, Math. Model. Nat. Phenom. 4(2) (2009), pp. 1-27.
2. C.W. Eurich, A. Thiel, and L. Fahse, Distributed delays stabilize ecological feedback systems, Phys. Rev. Lett. 94(15) (2005), p. 158104.
3. F.M. Atay, Delayed feedback control near Hopf bifurcation, Discrete Contin. Dyn. Syst. Ser. S 1(2) (2008), pp. 197-205.
4. W. Michiels, V. Van Assche, and S.-I. Niculescu, Stabilization of time-delay systems with a controlled time-varying delay and applications, IEEE Trans. Automat. Contr. 50(4) (2005), pp. 493-504. (Pubitemid 40555771)
5. R. Sipahi, F.M. Atay, and S.-I. Niculescu, Stability of traffic flow behaviour with distributed delays modeling the memory effects of the drivers, SIAM J. Appl. Math. 68(3) (2007/08), pp. 738-759.
6. R. Miyazaki, Characteristic equation and asymptotic behaviour of delay-differential equation, Funkcialaj Ekvacioj 40 (1997), pp. 471-481.
7. S. Bernard, J. Bé lair, and M.C. Mackey, Sufficient conditions for stability of linear differential equations with distributed delay, Discrete Contin. Dyn. Syst. Ser. B 1(2) (2001), pp. 233-256. (Pubitemid 33771907)
8. G. Kiss and B. Krauskopf, Stability implications of delay distribution for first-order and secondorder systems, Discrete Contin. Dyn. Syst. Ser. B 13(2) (2009), pp. 327-345.
9. G. Kiss and B. Krauskopf, Stabilizing effect of delay distribution on a second-order scalar delay equation, in Eigth IFAC Workshop on Time Delay Systems, S.I. Niculescu and V. Rasvan, eds., IFAC, Oxford, 2009.
10. O.S. Bursi, A. Gonzalez-Buelga, L. Vulcan, S.A. Neild, and D.J. Wagg, Novel coupling Rosenbrock-based algorithms for real-time dynamic substructure testing, Earthquake Eng. Struct. Dyn. 37(3) (2007), pp. 339-360. (Pubitemid 351330768)
11. M.I. Wallace, J. Sieber, A. Neild, D.J. Wagg, and B. Krauskopf, Stability analysis of real-time dynamic substructuring using delay differential equation models, Earthquake Eng. Struct. Dyn. 34(15) (2005), pp. 1817-1832. (Pubitemid 41741682)
12. Y.N. Kyrychko, S.J. Hogan, A. Gonzalez-Buelga, and D.J. Wagg, Modelling real-time dynamic substructuring using partial delay differential equations, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463(2082) (2007), pp. 1509-1523.
13. Y.N. Kyrychko, K.B. Blyuss, A. Gonzalez-Buelga, S.J. Hogan, and D.J. Wagg, Real-time dynamic substructuring in a coupled oscillator-pendulum system, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462(2068) (2006), pp. 1271-1294. (Pubitemid 44922117)
14. O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel, and Hans-Otto. Walther, Delay Equations, Applied Mathematical Sciences, Vol. 110, Springer-Verlag, New York, 1995.
15. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Applied Mathematical Sciences, Vol. 99, Springer-Verlag, New York, 1993.
16. G. Stépá n, Retarded Dynamical Systems: Stability and Characteristic Functions, Pitman Research Notes in Mathematics Series, Vol. 210, Longman Scientific & Technical, Harlow, 1989.
17. Y. Kuang, Nonoccurrence of stability switching in systems of differential equations with distributed delays, Quart. Appl. Math. LII(3) (1994), pp. 569-578.
18. L.S. Pontryagin, On the zeros of some elementary transcendental functions, Amer. Math. Soc. Trans. 1(2) (1955), pp. 95-110.