Stabilization of structurally damped systems by pointwise time-delayed feedback control. (English) Zbl 0969.93030
The authors study a class of multidimensional damped distributed parameter systems with pointwise time-delayed displacement. They transform the linear system with delayed control action into an equivalent system without delays and show that the feedback gain control exists and asymptotically stabilizes the closed-loop modal system.
Finally specific numerical results for a structurally damped beam are obtained.
Finally specific numerical results for a structurally damped beam are obtained.
Reviewer: Stefan Zanfir (Craiova)
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C23 | Control/observation systems governed by functional-differential equations |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
stabilization; multidimensional damped distributed parameter systems; pointwise time-delayed displacement; delayed control; damped beamReferences:
| [1] | Datko, R.; Lagnese, J.; Polis, M. P., An example on the effect of time delays in boundary-feedback stabilization of wave equations, SIAM J. Control Optim., 24, 152-156 (1986) · Zbl 0592.93047 |
| [2] | Datko, R., Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks, SIAM J. Control Optim., 2, 697-713 (1988) · Zbl 0643.93050 |
| [3] | R. Bellman, K.L. Cooke, Differential-Difference Equations, Academic Press, New York, 1963.; R. Bellman, K.L. Cooke, Differential-Difference Equations, Academic Press, New York, 1963. · Zbl 0105.06402 |
| [4] | Bose, F. G., Stability conditions for the general linear difference-differential equation with constant coefficients and one constant delay, J. Math. Anal. Appl., 140, 136-176 (1989) · Zbl 0681.34063 |
| [5] | Fiagbedzi, Y. A.; Pearson, A. E., Feedback stabilization of linear autonomous time lag systems, IEEE Trans. Automat. Control, 31, 847-855 (1986) · Zbl 0601.93045 |
| [6] | Gopalsamy, K.; Zhang, B. G., On delay differential equations with impulses, J. Math. Anal. Appl., 139, 110-122 (1989) · Zbl 0687.34065 |
| [7] | Sadek, I. S.; Sloss, J. M.; Bruch, J. C.; Adali, S., Dynamically loaded beam subject to time-delayed active control, Mech. Res. Commun., 10, 81-87 (1989) · Zbl 0676.73062 |
| [8] | Abdel-Rohman, M., Time-delayed effects on actively damped structures, ASCE J. Eng. Mech., 113, 1709-1719 (1987) |
| [9] | Sloss, J. M.; Sadek, I. S.; Bruch, J. C.; Adali, S., Stabilization of structurally damped systems by time-delayed feedback control, Dynamics Stability Systems, 7, 173-188 (1992) · Zbl 0771.93031 |
| [10] | Sloss, J. M.; Sadek, I. S.; Bruch, J. C.; Adali, S., The effects of the delayed active displacement control and damped structures, Control Theory Adv. Tech., 10, 973-992 (1995) |
| [11] | C. Abdallah, P. Dorato, J. Benitez-Read, R. Byrne, Delayed positive feedback can stabilize oscillatory systems, Proceedings of the American Control Conference, San Francisco, CA, vol. 3, 1993, pp. 3106-3107.; C. Abdallah, P. Dorato, J. Benitez-Read, R. Byrne, Delayed positive feedback can stabilize oscillatory systems, Proceedings of the American Control Conference, San Francisco, CA, vol. 3, 1993, pp. 3106-3107. |
| [12] | Z. Artstein, Linear system with delayed controls: A reduction, IEEE Trans. Automat. Control AC-27(4) (1982) 869-879.; Z. Artstein, Linear system with delayed controls: A reduction, IEEE Trans. Automat. Control AC-27(4) (1982) 869-879. · Zbl 0486.93011 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
