# On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls

Open Mathematics (2003)

- Volume: 1, Issue: 2, page 141-156
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topL. Fardigola. "On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls." Open Mathematics 1.2 (2003): 141-156. <http://eudml.org/doc/268684>.

@article{L2003,

abstract = {},

author = {L. Fardigola},

journal = {Open Mathematics},

keywords = {93D15; 35B37; 35A22},

language = {eng},

number = {2},

pages = {141-156},

title = {On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls},

url = {http://eudml.org/doc/268684},

volume = {1},

year = {2003},

}

TY - JOUR

AU - L. Fardigola

TI - On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls

JO - Open Mathematics

PY - 2003

VL - 1

IS - 2

SP - 141

EP - 156

AB -

LA - eng

KW - 93D15; 35B37; 35A22

UR - http://eudml.org/doc/268684

ER -

## References

top- [1] R. Bellman and K.L. Cook: Differential-Difference Equations, Acad. Press, New York-London, 1963.
- [2] R.F. Curtain and A.J. Pritchard: “Robust stabilization of infinite-dimensional systems with respect to coprime factor perturbations”, In: Differential equations, dynamical systems, and control science. A Festschrift in Honor of Lawrence Markus. Marcel Dekker. Lect. Notes Pure Appl. Math., New York, NY, Vol. 152, (1994), pp. 437–456. Zbl0792.93097
- [3] R. Datko, J. Lagnese, M.P. Polis: “An example of the effect of time delays in boundary feedback stabilization of wave equations”, SIAM J. Control. Optim., Vol. 24, (1986), pp. 152–156. http://dx.doi.org/10.1137/0324007 Zbl0592.93047
- [4] L.V. Fardigola: “On a nonlocal two-point boundary-value problem in a layer for an equation with variable coefficients” (in Russian), Sibirsk. Mat. Zh., Vol. 38, (1997), pp. 424–438, English translation in: Siberian Math. J., Vol. 38, (1997), pp. 367–379.
- [5] L.V. Fardigola: “On stabilizability of evolution systems of partial differential equations on ℝn ×[0,+∞) by feedback control”, Visnyk Kharkivs'kogo Universytetu. Ser. Matematyka, Prykladna Matematyka i Mekhanika, Vol. 475, (2000), pp. 183–194.
- [6] L.V. Fardigola: “A criterion for stabilizability of differential equations with constant coefficients on the whole space”, (in Russian), Differ. uravn., Vol. 36, (2000), pp. 1699–1706, English translation in: Differ. Equ., Vol. 36, (2000), pp. 1863–1871. Zbl1017.78522
- [7] I.M. Gelfand and G.E. Shilov: Generalized Functions (in Russian), Vol. 3, Moskow, 1958.
- [8] L. Hörmander: The analysis of linear differential operators. V. 2: Differential operators with constant coefficients, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. Zbl0521.35002
- [9] L. Hörmander: “On the division of distributions by polynomials”, Ark. Mat., Vol. 3, (1958), pp. 555–568. Zbl0131.11903
- [10] N. Levan: “The left shift semigroup approach to stability of distributed systems”, J. Math. Anal. Appl., Vol. 152, (1990), pp. 354–367. http://dx.doi.org/10.1016/0022-247X(90)90070-V Zbl0783.47055
- [11] S. Łojasiewicz: “Sur le problème de la division”, Studia Math., Vol. 18, (1959), pp. 87–136. Zbl0115.10203
- [12] H. Logemann: “Destabilizing effect of small time delays on feedback controlled descriptor systems”, Linear Algebra and its Appl., Vol. 272, (1998), pp. 131–153. http://dx.doi.org/10.1016/S0024-3795(97)00328-5
- [13] L. Pandolfi: “On feedback stabilization of functional differential equations”, Boll. Unione Mat. Ital., IV Ser. 11, Suppl. Fasc., Vol. 3, (1975), pp. 626–635. Zbl0318.93027
- [14] I.G. Petrowsky: “On the Cauchy problem for systems of linear partial differential equations in a domain of nonanalitic functions”, Bull. Mosk. Univ., Ser. A, No. 7, (1938), pp. 1–72.
- [15] L.S. Pontriagin: “On zeroz on some elementary transcendence functions”, Izv. AN SSSR, Ser. Mat., Vol. 6, (1942), pp. 115–134.
- [16] R. Rebarber and S. Townley: “Robustness with respect to delay for exponential stability of distributed parameter systems”, SIAM J. Contr. Optim., Vol. 37, (1998), pp. 230–244. http://dx.doi.org/10.1137/S0363012996312453 Zbl0919.93041
- [17] A. Seidenberg: “A new decision method for elementary algebra”, Ann. Math., Vol. 2, (1954), pp. 365–374. http://dx.doi.org/10.2307/1969640 Zbl0056.01804
- [18] J.M. Sloss, I.S. Sadek, J.C. Bruch, S. Aldali: “Stabilization of structurally damped systems by time-delayed feedback control”, Dyn. Stab. Syst., Vol. 7, (1992), pp. 173–178. Zbl0771.93031
- [19] C.C. Travis and G.F. Webb: “Existence and stability for partial functional differential equations”, Trans. Am. Math, Soc., Vol. 200, (1974), pp. 395–418. http://dx.doi.org/10.2307/1997265 Zbl0299.35085

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.