Impulsive stabilization of high-order nonlinear retarded differential equations

Juan Liu; Xiaodi Li

Applications of Mathematics (2013)

  • Volume: 58, Issue: 3, page 347-367
  • ISSN: 0862-7940

Abstract

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In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods.

How to cite

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Liu, Juan, and Li, Xiaodi. "Impulsive stabilization of high-order nonlinear retarded differential equations." Applications of Mathematics 58.3 (2013): 347-367. <http://eudml.org/doc/252523>.

@article{Liu2013,
abstract = {In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods.},
author = {Liu, Juan, Li, Xiaodi},
journal = {Applications of Mathematics},
keywords = {high-order nonlinear retarded differential equation; Lyapunov function; impulsive stabilization; exponential stability; higher-order nonlinear retarded differential equation; Lyapunov function; impulsive stabilization; exponential stability},
language = {eng},
number = {3},
pages = {347-367},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Impulsive stabilization of high-order nonlinear retarded differential equations},
url = {http://eudml.org/doc/252523},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Liu, Juan
AU - Li, Xiaodi
TI - Impulsive stabilization of high-order nonlinear retarded differential equations
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 347
EP - 367
AB - In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods.
LA - eng
KW - high-order nonlinear retarded differential equation; Lyapunov function; impulsive stabilization; exponential stability; higher-order nonlinear retarded differential equation; Lyapunov function; impulsive stabilization; exponential stability
UR - http://eudml.org/doc/252523
ER -

References

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  1. Bainov, D. D., Simeonov, P. S., Systems with Impulsive Effect: Stability, Theory and Applications, Ellis Horwood New York (1989). (1989) MR1010418
  2. Fu, X., Yan, B., Liu, Y., Introduction of Impulsive Differential Systems, Science Press Beijing (2005). (2005) 
  3. Gimenes, L. P., Federson, M., 10.1016/j.amc.2005.10.038, Appl. Math. Comput. 177 (2006), 44-62. (2006) Zbl1105.34049MR2234496DOI10.1016/j.amc.2005.10.038
  4. Gimenes, L. P., Federson, M., Táboas, P., 10.1016/j.na.2006.06.006, Nonlinear Anal., Theory Methods Appl. 67 (2007), 545-553. (2007) Zbl1125.34061MR2317186DOI10.1016/j.na.2006.06.006
  5. Khadra, A., Liu, X., Shen, X., 10.1109/TCSI.2003.808839, IEEE Trans. Circuits Systems I Fund. Theory Appl. 50 (2003), 341-351. (2003) MR1984762DOI10.1109/TCSI.2003.808839
  6. Lakshmikantham, V., Bajnov, D. D., Simeonov, P. S., Theory of Impulsive Differential Equations, World Scientific Singapore (1989). (1989) Zbl0719.34002MR1082551
  7. Li, X., 10.1002/mma.1278, Math. Methods Appl. Sci. 33 (2010), 1596-1604. (2010) Zbl1247.34026MR2680669DOI10.1002/mma.1278
  8. Li, X., New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays, Nonlinear Anal., Real World Appl. 11 (2010), 4194-4201. (2010) Zbl1210.34103MR2683867
  9. Li, X., Weng, P., Impulsive stabilization of a class of nonlinear differential equations, Appl. Math., Ser. A (Chin. Ed.) 18 (2003), 408-416. (2003) Zbl1050.34087MR2023583
  10. Liu, X., 10.1216/rmjm/1181072290, Rocky Mt. J. Math. 25 (1995), 381-395. (1995) Zbl0832.34039MR1340015DOI10.1216/rmjm/1181072290
  11. Liu, X., Ballinger, G., 10.1016/S0362-546X(01)00847-1, Nonlinear Anal., Theory Methods Appl. 51 (2002), 633-647. (2002) Zbl1015.34069MR1920341DOI10.1016/S0362-546X(01)00847-1
  12. Luo, Z., Shen, J., 10.1016/S0893-9659(03)00069-7, Appl. Math. Lett. 16 (2003), 695-701. (2003) Zbl1068.93054MR1986037DOI10.1016/S0893-9659(03)00069-7
  13. Prussing, J. E., Wellnitz, L. J., Heckathorn, W. G., 10.2514/3.20436, J. Guidance Control Dynam. 12 (1989), 487-494. (1989) MR1005019DOI10.2514/3.20436
  14. Weng, A., Sun, J., Impulsive stabilization of second-order delay differential equations, Nonlinear Anal., Real World Appl. 8 (2007), 1410-1420. (2007) Zbl1136.93036MR2344990
  15. Yang, T., Impulsive Systems and Control: Theory and Applications, Nova Science Publishers New York (2001). (2001) 
  16. Zhang, H., Jiao, J., Chen, L., 10.1016/j.biosystems.2006.09.038, BioSystems 90 (2007), 350-361. (2007) DOI10.1016/j.biosystems.2006.09.038

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