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2019 | Vol. 68, nr 3 | 553--564
Tytuł artykułu

Exponential stability of impulsive delayed nonlinear hybrid differential systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In recent years, with the rapid development of digital components, digital electronic computers, especially microprocessors, digital controllers have replaced analog controllers on many occasions. The application of digital controller makes the performance analysis of impulsive system more and more important. This paper considers global exponential stability (GES) of impulsive delayed nonlinear hybrid differential systems (IDNHDS).Through the application of the Lyapunov method and the Razumikhin technique, a series of uncomplicated and useful guiding principles have been obtained. The results of a numerical simulation are presented to demonstrate that the method is correct and effective.
Wydawca

Rocznik
Strony
553--564
Opis fizyczny
Bibliogr. 24 poz., rys., wz.
Twórcy
  • Tianjin University Tianjin, China, jqqhb@163.com
  • Zhonghuan Information College, Tianjin University of Technology Tianjin, China
  • Tianjin University Tianjin, China
Bibliografia
  • [1] Yu H.G., Zhong S.M., Ye M., Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay, Mathematics and Computers in Simulation, vol. 80, no. 3, pp. 619–632 (2009).
  • [2] Stamova I.M., Stamov G.T., LyapunovCRazumikhin method for impulsive functional differential equations and applications to the population dynamics, Journal of Computational and Applied Mathematics, vol. 130, no. 1–2, pp. 163–171 (2001).
  • [3] Zhou J., Xiang L., Liu Z.R., Synchronization in complex delayed dynamical networks with impulsive effects, Physica A: Statistical Mechanics and its Applications, vol. 384, no. 2, pp. 684–692 (2007).
  • [4] Zhou J., Chen T.P., Xiang L., Liu M.C., Global Synchronization of Impulsive Coupled Delayed Neural Networks, Lecture Notes in Computer Science, Advances in Neural Networks, vol. 3971, pp. 303–308 (2006).
  • [5] Guo J.F., Gao C.C., Output Variable Structure Control for Time-Invariant Linear Time-Delay Singular System, Journal of Systems Science and Complexity, vol. 20, no. 3, pp. 454–460 (2007).
  • [6] Liu X.Z.,Wang Q., The method of Lyapunov functionals and exponential stability of impulsive systems with time delay, Nonlinear Analysis, vol. 66, no. 7, pp. 1465–1484 (2007).
  • [7] Zhang Y., Sun J.T., Stability of impulsive linear differential equations with time delay, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 52, no. 10, pp. 701–705 (2005).
  • [8] Liu X.Z., Ballinger G., Uniform asymptotic stability of impulsive delay differential equations, Computers and Mathematics with Applications, vol. 41, no. 7, pp. 903–915 (2007).
  • [9] Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of Impulsive Differential Equations, Book Series: Series in Modern Applied Mathematics (1989).
  • [10] Fu X.L., Li X.D., Razumikhin-type theorems on exponential stability of impulsive infinite delay differential systems, Journal of Computational and Applied Mathematics, vol. 224, no. 1, pp. 1–10 (2009).
  • [11] Wu Q.J., Zhou J., Xiang L., GES of impulsive differential equations with any time delays, Applied Mathematics Letters, vol. 23, no. 2, pp. 143–147 (2010).
  • [12] Wang Q., Liu X.Z., Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method, Applied Mathematics Letters, vol. 20, no. 8, pp. 839–845 (2007).
  • [13] Ye H., Michel A.N., Hou L., Stability theory for hybrid dynamical systems, IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 461–474 (1998).
  • [14] Goebel R., Teel A.R., Results on solution sets to hybrid systems with applications to stability theory, Proceedings of the 2005 American Control Conference, pp. 557–562 (2005).
  • [15] Lakshmikantham V., Liu X., Impulsive hybrid systems and stability theory, Dynamical systems application, vol. 7, no. 1, pp. 1–9 (1998).
  • [16] Guan Z.H., Hill D.J., Shen X.M., On hybrid impulsive and switching systems and application to nonlinear control, IEEE Transactions on Automatic Control, vol. 50, no. 7, pp. 1058–1062 (2005).
  • [17] Liu B., Liu X.Z., Liao X.X., Stability and robustness of quasi-linear impulsive hybrid systems, Journal of Mathematical analysis and applications, vol. 238, no. 2, pp. 416–430 (2003).
  • [18] Hayakawa T., Haddad W.M., Volyanskyy K.Y., Neural network hybrid adaptive control for nonlinear uncertain impulsive dynamical systems,Nonlinear Analysis: Hybrid Systems, vol. 2, no. 3, pp. 862–874 (2008).
  • [19] Wang P.G., Liu X., New comparison principle and stability criteria for impulsive hybrid systems on time scales, Nonlinear Analysis: Real World Applications, vol. 7, no. 5, pp. 1096–1103 (2006).
  • [20] Attia S.A., Azhmyakov V., Raisch J., on an optimization problem for a class of impulsive hybrid systems, Discrete Event Dynamic Systems, vol. 20, no. 2, pp. 215–231 (2010).
  • [21] Liu X.Z., Shen J.H., Stability theory of hybrid dynamical systems with time delay, IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 620–625 (2006).
  • [22] Kaslik E., Sivasundaram S., Impulsive hybrid synchronization of chaotic discrete-time delayed neural networks, Neural Networks (IJCNN), The 2010 International Joint Conference, pp. 1-8 (2010).
  • [23] Li C.D., Ma F., Feng G., Hybrid impulsive and switching time-delay systems, IET Control Theory and Applications, vol. 3, no. 11, pp. 1487–1498 (2009).
  • [24] Zhang Y., Sun J.T., Stability of impulsive linear hybrid systems with time delay, Journal of Systems Science and Complexity, vol. 23, no. 4, pp. 738–747 (2010).
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.baztech-e3e71821-24bd-40c4-96ff-6e1daa15093c
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