http://iet.metastore.ingenta.com
1887

Exponential stability of impulsive systems with random delays under sampled-data control

Exponential stability of impulsive systems with random delays under sampled-data control

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this study, the exponential stability problem of impulsive system is investigated via sampled-data control in the presence of random time-varying delays and non-linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled-data controller to ensure an exponential stability for the closed-loop system. By extending the first- and second-order reciprocal convex approach, an efficient method called third-order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay-dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique.

References

    1. 1)
      • 1. Xiong, W., Zhang, D., Cao, J.: ‘Impulsive synchronisation of singular hybrid coupled networks with time-varying nonlinear perturbation’, Int. J. Syst. Sci., 2017, 48, (2), pp. 417424.
    2. 2)
      • 2. Zhang, W., Tang, Y., Miao, Q., et al.: ‘Synchronization of stochastic dynamical networks under impulsive control with time delays’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, (10), pp. 17581768.
    3. 3)
      • 3. Zhang, W., Tang, Y., Wu, X., et al.: ‘Synchronization of nonlinear dynamical networks with heterogeneous impulses’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2014, 61, (4), pp. 12201228.
    4. 4)
      • 4. Zhu, Q.: ‘pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching’, J. Franklin Inst., 2014, 351, (7), pp. 39653986.
    5. 5)
      • 5. Zhu, Q., Song, B.: ‘Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays’, Nonlinear Anal., Real World Appl., 2011, 12, (5), pp. 28512860.
    6. 6)
      • 6. Bainov, D., Simeonov, P.: ‘Systems with impulse effects: stability, theory and applications’ (Academy Press, 1989).
    7. 7)
      • 7. Liu, B., Liu, X., Chen, G., et al.: ‘Robust impulsive synchronization of uncertain dynamical networks’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2005, 52, (7), pp. 14311441.
    8. 8)
      • 8. Rogovchenko, Y.V.: ‘Impulsive evolution systems: main results and new trends’, Dyn. Continuous Discret. Impulsive Syst., 1997, 3, (1), pp. 5788.
    9. 9)
      • 9. Zhu, Q., Cao, J.: ‘Robust exponential stability of Markovian jump impulsive stochastic Cohen–Grossberg neural networks with mixed time delays’, IEEE Trans. Neural Netw., 2010, 21, (8), pp. 13141325.
    10. 10)
      • 10. Zheng, C.D., Xian, Y., Wang, Z.: ‘Third-order reciprocally convex approach to stability of fuzzy cellular neural networks under impulsive perturbations’, Soft Comput., 2017, 21, (3), pp. 699720.
    11. 11)
      • 11. Gao, S., Chen, L., Nieto, J.J., et al.: ‘Analysis of a delayed epidemic model with pulse vaccination and saturation incidence’, Vaccine, 2006, 24, (35), pp. 60376045.
    12. 12)
      • 12. Balasubramaniam, P., Krishnasamy, R.: ‘Robust exponential stabilization results for impulsive neutral time-delay systems with sector-bounded nonlinearity’, Circuits Syst. Signal Process., 2014, 33, pp. 27412759.
    13. 13)
      • 13. Mathiyalagan, K., Su, H., Shi, P., et al.: ‘Exponential H filtering for discrete-time switched neural networks with random delays’, IEEE Trans. Cybern., 2015, 45, (4), pp. 676687.
    14. 14)
      • 14. Peng, C., Zhang, J.: ‘Delay-distribution-dependent load frequency control of power systems With probabilistic interval delays’, IEEE Trans. Power Syst., 2016, 31, (4), pp. 33093317.
    15. 15)
      • 15. Sakthivel, R., Selvi, S., Mathiyalagan, K., et al.: ‘Reliable mixed and passivity-based control for fuzzy Markovian switching systems with probabilistic time delays and actuator failures’, IEEE Trans. Cybern., 2015, 45, (12), pp. 27202731.
    16. 16)
      • 16. Krishnasamy, R., Balasubramaniam, P.: ‘A descriptor system approach to the delay-dependent exponential stability analysis for switched neutral systems with nonlinear perturbations’, Nonlinear Anal., Hybrid Syst., 2015, 15, pp. 2336.
    17. 17)
      • 17. Lian, J., Wang, M.: ‘Sliding-mode control of switched delay systems with nonlinear perturbations: average dwell time approach’, Nonlinear Dyn., 2010, 62, (4), pp. 791798.
    18. 18)
      • 18. Liu, J., Yue, D.: ‘Event-based fault detection for networked systems with communication delay and nonlinear perturbation’, J. Franklin Inst., 2013, 350, (9), pp. 27912807.
    19. 19)
      • 19. Rakkiyappan, R., Lakshmanan, S., Sivasamy, R., et al.: ‘Leakage-delay-dependent stability analysis of Markovian jumping linear systems with time-varying delays and nonlinear perturbations’, Appl. Math. Model., 2016, 40, (7), pp. 50265043.
    20. 20)
      • 20. Rakkiyappan, R., Dharani, S., Zhu, Q.: ‘Synchronization of reaction-diffusion neural networks with time-varying delays via stochastic sampled-data controller’, Nonlinear Dyn., 2015, 79, (1), pp. 485500.
    21. 21)
      • 21. Rakkiyappan, R., Sakthivel, N.: ‘Pinning sampled-data control for synchronization of complex networks with probabilistic time-varying delays using quadratic convex approach’, Neurocomputing, 2015, 162, pp. 2640.
    22. 22)
      • 22. Sakthivel, R., Arunkumar, A., Mathiyalagan, K.: ‘Robust sampled-data H control for mechanical systems’, Complexity, 2015, 20, (4), pp. 1929.
    23. 23)
      • 23. Shi, K., Liu, X., Zhu, H., et al.: ‘Novel integral inequality approach on master-slave synchronization of chaotic delayed Lur'e systems with sampled-data feedback control’, Nonlinear Dyn., 2016, 83, (3), pp. 12591274.
    24. 24)
      • 24. Song, Q., Liu, F., Wen, G., et al.: ‘Synchronization of coupled harmonic oscillators via sampled position data control’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2016, 63, (7), pp. 10791088.
    25. 25)
      • 25. Wu, Z.G., Shi, P., Su, H., et al: ‘Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data’, IEEE Trans. Cybern., 2013, 43, (6), pp. 17961806.
    26. 26)
      • 26. Seuret, A., Gouaisbaut, F.: ‘Wirtinger-based integral inequality: application to time-delay systems’, Automatica, 2013, 49, pp. 28602866.
    27. 27)
      • 27. Chandrasekar, A., Rakkiyappan, R., Cao, J., et al.: ‘Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach’, IEEE Trans. Neural Netw., 2014, 57, pp. 7993.
    28. 28)
      • 28. Park, P., Ko, J.W., Jeong, C.: ‘Reciprocally convex approach to stability of systems with time-varying delays’, Automatica, 2011, 47, (1), pp. 235238.
    29. 29)
      • 29. Lee, W.I., Park, P.: ‘Second-order reciprocally convex approach to stability of systems with interval time-varying delays’, Appl. Math. Comput., 2014, 229, pp. 245253.
    30. 30)
      • 30. Wang, H., Duan, S., Li, C., et al.: ‘Globally exponential stability of delayed impulsive functional differential systems with impulse time windows’, Nonlinear Dyn., 2016, 84, (3), pp. 16551665.
    31. 31)
      • 31. Boyd, S., Ghaoui, L.E., Feron, E., et al.: ‘Linear matrix inequalities in system and control theory’ (SIAM, Philadelphia, PA, 1994).
    32. 32)
      • 32. Liu, Y., Hu, L.-S., Shi, P.: ‘A novel approach on stabilization for linear systems with time-varying input delay’, Appl. Math. Comput., 2012, 218, pp. 59375947.
    33. 33)
      • 33. Revathi, V.M., Balasubramaniam, P., Park, J.H., et al: ‘Hfiltering for sample data systems with stochastic sampling and Markovian jumping parameters’, Nonlinear Dyn., 2014, 78, (2), pp. 813830.
    34. 34)
      • 34. Zhang, W., Tang, Y., Miao, Q., et al: ‘Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects’, IEEE Trans. Neural Netw. Learn. Syst., 2013, 24, (8), pp. 13161326.
    35. 35)
      • 35. Hua, C., Ge, C., Guan, X.: ‘Synchronization of chaotic Lur'e systems with time delays using sampled-data control’, IEEE Trans. Neural Netw. Learn. Syst., 2015, 26, (6), pp. 12141221.
    36. 36)
      • 36. Guan, Z.-H., Han, G.-S., Li, J., et al: ‘Impulsive multiconsensus of second-order multiagent networks using sampled position data’, IEEE Trans. Neural Netw. Learn. Syst., 2015, 26, (11), pp. 26782688.
    37. 37)
      • 37. Lakshmanan, S., Park, J.H., Rihan, F.A., et al: ‘Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control’, Chin. Phys. B, 2014, 23, (7), p. 070205.
    38. 38)
      • 38. Lee, L., Liu, Y., Liang, J., et al: ‘Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems’, ISA Trans., 2015, 57, pp. 172178.
    39. 39)
      • 39. Naghshtabrizi, P., Hespanha, J.P., Teel, A.R.: ‘Exponential stability of impulsive systems with application to uncertain sampled-data systems’, Syst. Control Lett., 2008, 57, (5), pp. 378385.
    40. 40)
      • 40. Xu, S., Chen, T.: ‘Robust H filtering for uncertain impulsive stochastic systems under sampled measurements’, Automatica (J. IFAC), 2003, 39, (3), pp. 509516.
    41. 41)
      • 41. Qiu, F., Cao, J.: ‘Exponential stability and L2-gain analysis for sampled-data control of linear systems’, J. Franklin Inst., 2016, 353, (2), pp. 462477.
    42. 42)
      • 42. Wu, W., Reimann, S., Gorges, D., et al: ‘Suboptimal event-triggered control for time-delayed linear systems’, IEEE Trans. Autom. Control, 2015, 60, (5), pp. 13861391.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0503
Loading

Related content

content/journals/10.1049/iet-cta.2017.0503
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address