Stability analysis for neutral stochastic linear system

Boren Li; Xueliang Liu

Stability analysis for neutral stochastic linear system

View Fulltext

Author(s): Boren Li ¹ and Xueliang Liu ¹
- Affiliations: 1: College of Computer, Dongguan University of Technology, Dongguan, Guangdong 523808, People's Republic of China
Source: Volume 9, Issue 16, 29 October 2015, p. 2474 – 2481
DOI: 10.1049/iet-cta.2014.1377 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 05/07/2014, Accepted 26/06/2015, Revised 24/04/2015, Published 29/07/2015

This study is a further note on stability analysis for uncertain linear neutral stochastic system. Firstly, the stability of linear neutral stochastic system with mix delays is studied. By employing a new Lyapunov–Krasovskii functional and novel method to estimate the integral terms, the less conservative stability criteria are obtained. Compared with previous results, the novel method can sufficiently utilise more negative items information. Then, in virtue of the Schur complement and linear matrix inequality technique, the robust stability of the uncertain neutral stochastic system is derived, which have less conservatism. Finally, two numerical examples show that the authors’ results are effective and less conservative than other reports in the previous literature.

References

1. 1)
  - 19. Seuret, A., Gouaisbaut, F.: ‘On the use of the Wirtinger inequalities for time-delay systems’. Proc. of the 10th IFAC Workshop on Time Delay Systems, Boston, USA, June 2012, pp. 260–265.
2. 2)
  - 7. Deng, F.Q., Mao, W.H., Wan, A.H.: ‘A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems’, Appl. Math. Comput., 2013, 221, pp. 132–143 (doi: 10.1016/j.amc.2013.05.071).
3. 3)
  - 1. Li, H., Li, H.B., Zhong, S.M.: ‘Stability of neutral type descriptor system with mixed delays’, Chaos Solitons Fractals, 2007, 33, pp. 1796–1800 (doi: 10.1016/j.chaos.2006.03.055).
4. 4)
  - 11. Yu, K.W., Lien, C.H.: ‘Stability criteria for uncertain neutral systems with interval time-varying delays’, Chaos Solitons Fractals, 2008, 38, pp. 650–657 (doi: 10.1016/j.chaos.2007.01.002).
5. 5)
  - 8. Wang, W.Q., Nguang, S.K., Zhong, S.M., Liu, F.: ‘Novel delay-dependent stability criterion for time-varying delay systems with parameter uncertainties and nonlinear perturbations’, Inf. Sci., 2014, 281, pp. 321–333 (doi: 10.1016/j.ins.2014.05.048).
6. 6)
  - 17. Su, W., Chen, Y.: ‘Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays’, Commun. Nonlinear Sci. Numer. Simul., 2009, 14, pp. 1576–1581 (doi: 10.1016/j.cnsns.2008.04.001).
7. 7)
  - 22. Gu, K., Kharitonov, V., Chen, J.: ‘Stability of time-delay systems’ (Birkhauser, Boston, 2003).
8. 8)
  - 23. Xie, L.: ‘Output feedback H∞ control of systems with parameter uncertainty’, Int. J. Control, 1996, 63, pp. 741–750 (doi: 10.1080/00207179608921866).
9. 9)
  - 10. Wang, W.Q., Nguang, S.K., Zhong, S.M., Liu, F.: ‘New delay-dependent stability criteria for uncertain neutral system with time-varying delays and nonlinear perturbations’, Circuits Syst. Signal Process., 2014, 33, pp. 2719–2740 (doi: 10.1007/s00034-014-9770-0).
10. 10)
  - 21. Chen, H.B.: ‘New results on stability analysis for neutral stochastic linear system’, IET Control Theory Appl., 2013, 7, pp. 1753–1764 (doi: 10.1049/iet-cta.2013.0008).
11. 11)
  - 17. Seuret, A., Gouaisbaut, F.: ‘Wirtinger-based integral inequality: application to time-delay systems’, Automatica, 2013, 49, (9), pp. 2860–2866 (doi: 10.1016/j.automatica.2013.05.030).
12. 12)
  - 18. Zhu, Q., Cao, J.: ‘Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays’, Neurocomputing, 2010, 73, pp. 2671–2680 (doi: 10.1016/j.neucom.2010.05.002).
13. 13)
  - 15. Chen, H.B., Zhang, Y., Hu, P.: ‘Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks’, Neurocomputing, 2010, 73, pp. 2554–2561 (doi: 10.1016/j.neucom.2010.06.003).
14. 14)
  - 13. Xu, S.Y., Shi, P., Chu, Y.M., Zou, Y.: ‘Robust stochastic stabilization and H∞ control of uncertain neutral stochastic time-delay systems’, J. Math. Anal. Appl., 2006, 314, pp. 1–16 (doi: 10.1016/j.jmaa.2005.03.088).
15. 15)
  - 12. Liu, Z.W., Zhang, H.G.: ‘Delay-dependent stability for systems with fast-varying neutral-type delays via PTVD compensation’, Acta Autom. Sin., 2010, 36, pp. 147–152.
16. 16)
  - 9. Lu, R.Q., Wu, H.Y., Bai, J.J.: ‘New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays’, J. Franklin Inst., 2014, 351, pp. 1386–1399 (doi: 10.1016/j.jfranklin.2013.11.001).
17. 17)
  - 3. Chen, Y., Zheng, W.X., Xue, A.K.: ‘A new result on stability analysis for stochastic neutral systems’, Automatica, 2010, 46, pp. 2100–2104 (doi: 10.1016/j.automatica.2010.08.007).
18. 18)
  - 4. Zhang, W.A., Li, Y.: ‘Delay-dependent robust stability of neutral systems with mixed delays and nonlinear perturbations’, Acta Autom. Sin., 2007, 33, pp. 863–866 (doi: 10.1360/aas-007-0863).
19. 19)
  - 8. Liu, X.-G., Wu, M., Martin, R., Tang, M.-L.: ‘Stability analysis for neutral systems with mixed delays’, J. Comput. Appl. Math., 2007, 202, (2), pp. 478–497 (doi: 10.1016/j.cam.2006.03.003).
20. 20)
  - 2. Qiu, F., Cui, B.T., Ji, Y.: ‘Novel robust stability analysis for uncertain neutral system with mixed delays’, Chaos Solitons Fractals, 2009, 42, pp. 1820–1828 (doi: 10.1016/j.chaos.2009.03.091).
21. 21)
  - 16. Park, J., Kwon, O.: ‘Analysis on global stability of stochastic neural networks of neutral type’, Mod. Phys. Lett., 2008, 22, pp. 3159–3170 (doi: 10.1142/S0217984908017680).
22. 22)
  - 14. Xu, S.Y., Chu, Y.M., Lu, J., Zou, Y.: ‘Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays’, IEEE Trans. Syst. Man Cybern. A, 2006, 36, pp. 540–548 (doi: 10.1109/TSMCA.2006.871648).
23. 23)
  - 6. Chen, H.B., Zhu, C.: ‘Delay-dependent exponential stability for uncertain neutral stochastic linear systems with interval time-varying delay’, IET Control Theory Appl., 2012, 6, pp. 2409–2418 (doi: 10.1049/iet-cta.2011.0517).

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Stability analysis for neutral stochastic linear system

References

Related content