Geodesic
Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems
Kybernetika, Tome 56 (2020) no. 4, pp. 753-766
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems, where the constrained time delay are considered in the conditions obtained. To protrude the availability of the devised stability scheme, simulation examples are ultimately demonstrated.
This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems, where the constrained time delay are considered in the conditions obtained. To protrude the availability of the devised stability scheme, simulation examples are ultimately demonstrated.
DOI : 10.14736/kyb-2020-4-0753
Classification : 34C15, 34D06, 34D35
Keywords: complex-variable system; delayed; uncertain; stability; aperiodically intermittent control 
@article{10_14736_kyb_2020_4_0753,
     author = {Zheng, Song},
     title = {Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems},
     journal = {Kybernetika},
     pages = {753--766},
     year = {2020},
     volume = {56},
     number = {4},
     doi = {10.14736/kyb-2020-4-0753},
     mrnumber = {4168534},
     zbl = {07286045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-4-0753/}
}
TY  - JOUR
AU  - Zheng, Song
TI  - Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems
JO  - Kybernetika
PY  - 2020
SP  - 753
EP  - 766
VL  - 56
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-4-0753/
DO  - 10.14736/kyb-2020-4-0753
LA  - en
ID  - 10_14736_kyb_2020_4_0753
ER  - 
%0 Journal Article
%A Zheng, Song
%T Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems
%J Kybernetika
%D 2020
%P 753-766
%V 56
%N 4
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-4-0753/
%R 10.14736/kyb-2020-4-0753
%G en
%F 10_14736_kyb_2020_4_0753
Zheng, Song. Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems. Kybernetika, Tome 56 (2020) no. 4, pp. 753-766. doi: 10.14736/kyb-2020-4-0753

[1] Cai, S., Zhou, P., Liu, Z.: Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control. Chaos 24 (2014), 033102. | DOI | MR

[2] Carr, T. W., Schwartz, I. B.: Controlling the unstable steady state in a multimode laser. Phys. Rev. E 51 (1995), 5109-5111. | DOI

[3] Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Trans. Circuits Systems I 54 (2007), 1317-1326. | DOI | MR

[4] Dong, Y., Liang, S., Guo, L., Wang, W.: Exponential stability and stabilization for uncertain discrete-time periodic systems with time-varying delay. IMA J. Math. Control Inform. 35 (2018), 3, 963-986. | DOI | MR

[5] Fang, T., Sun, J.: Stability of complex-valued impulsive system with delay. Appl. Math. Comput. 240 (2014), 102-108. | DOI | MR

[6] Fang, T., Sun, J.: Stability of complex-valued impulsive and switching system and application to the Lü system. Nonlinear Analysis: Hybrid Systems 14 (2015), 38-46. | DOI | MR

[7] Fowler, A. C., Gibbon, J. D., McGuinness, M. J.: The complex Lorenz equations. Physica D 4 (1982), 139-163. | DOI | MR | Zbl

[8] Huang, T., Li, C., Liu, X.: Synchronization of chaotic systems with delay using intermittent linear state feedback. Chaos 18 (2008), 033122. | DOI | MR

[9] Jiang, C., Zhang, F., Li, T.: Synchronization and antisynchronization of N-coupled fractional-order complex chaotic systems with ring connection. Math. Methods Appl. Sci. 41 (2018), 2625-2638. | DOI | MR

[10] Li, C. D., Liao, X. F., Huang, T. W.: Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17 (2007), 013103. | DOI | MR

[11] Li, N., Sun, H., Zhang, Q.: Exponential synchronization of united complex dynamical networks with multi-links via adaptive periodically intermittent control. IET Control Theory Appl. 159 (2013), 1725-1736. | DOI | MR

[12] Liang, Y., Wang, X.: Synchronization in complex networks with non-delay and delay couplings via intermittent control with two switched periods. Physica A 395 (2014), 434-444. | DOI | MR

[13] Liu, X., Chen, T.: Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans. Automat. Control 60 (2015), 3316-3321. | DOI | MR

[14] Liu, X., Liu, Y., Zhou, L.: Quasi-synchronization of nonlinear coupled chaotic systems via aperiodically intermittent pinning control. Neurocomputing 173 (2016), 759-767. | DOI

[15] Liu, L., Wang, Z., Huang, Z., Zhang, H.: Adaptive predefined performance control for IMO systems with unknown direction via generalized fuzzy hyperbolic model. IEEE Trans. Fuzzy Systems 25 (2007), 527-542. | DOI

[16] Mahmoud, G. M., Bountis, T., Mahmoud, E. E.: Active control and global synchronization for complex Chen and Lü systems. Int. J. Bifurcat. Chaos 17 (2014), 4295-4308. | DOI | MR

[17] Mahmoud, G., Mahmoud, E., Arafa, A.: On modified time delay hyperchaotic complex Lü system. Nonlinear Dynamics 80 (2015), 855-869. | DOI | MR

[18] Mahmoud, G., Mahmoud, E., Arafa, A.: Projective synchronization for coupled partially linear complex-variable systems with known parameters. Math. Methods Appl. Sci. 40 (2017), 1214-1222. | DOI | MR

[19] Ning, C. Z., Haken, H.: Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. Phys. Rev. A 41 (1990), 3826-3837. | DOI

[20] Ott, E., Grebogi, C., Yorke, J.: Controlling chaos. Phys. Rev. Lett. 64 (1990), 1196. | DOI | MR | Zbl

[21] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821-824. | DOI | MR | Zbl

[22] Qiu, J., Cheng, L., X, Chen, Lu, J., He, H.: Semi-periodically intermittent control for synchronization of switched complex networks: a mode-dependent average dwell time approach. Nonlinear Dynamics 83 (2016), 1757-1771. | DOI | MR

[23] Starrett, J.: Control of chaos by occasional bang-bang. Phys. Rev. E 67 (2003), 036203. | DOI

[24] Xia, W., Cao, J.: Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19 (2009), 013120. | DOI | MR

[25] Zheng, S.: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dynamics 74 (2013), 957-967. | DOI | MR | Zbl

[26] Zheng, S.: Impulsive complex projective synchronization in drive-response complex coupled dynamical networks. Nonlinear Dynamics 79 (2015), 147-161. | DOI | MR

[27] Zheng, S.: Stability of uncertain impulsive complex-variable chaotic systems with time- varying delays. ISA Trans. 58 (2015), 20-26. | DOI

[28] Zheng, S.: Further Results on the impulsive synchronization of uncertain complex-variable chaotic delayed systems. Complexity 21 (2016), 131-142. | DOI | MR

[29] Zheng, S.: Synchronization analysis of time delay complex-variable chaotic systems with discontinuous coupling. J. Franklin Inst. 353 (2016), 1460-1477. | DOI | MR

[30] Zheng, S.: Stability analysis of uncertain complex-variable delayed nonlinear systems via intermittent control with multiple switched periods. Kybernetika 54 (2018), 937-957. | DOI | MR

[31] Zheng, S., Bi, Q., Cai, G.: Adaptive projective synchronization in complex networks with time-varying coupling delay. Phys. Lett. A 373 (2009), 1553-1559. | DOI | MR

[32] Zochowski, M.: Intermittent dynamical control. Physica D 145 (2000), 181-190. | DOI

Cité par Sources :