Kybernetika 49 no. 5, 780-791, 2013

Stability analysis for neutral stochastic systems with mixed delays

Huabin Chen and Peng Hu


This paper is concerned with the problem of the exponential stability in mean square moment for neutral stochastic systems with mixed delays, which are composed of the retarded one and the neutral one, respectively. Based on an integral inequality, a delay-dependent stability criterion for such systems is obtained in terms of linear matrix inequality (LMI) to ensure a large upper bounds of the neutral delay and the retarded delay by dividing the neutral delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments. And the developed method can well reduce the conservatism compared with the existing results. Finally, an illustrative numerical example is given to show the effectiveness of our proposed method.


linear matrix inequality (LMI), neutral stochastic time-delay systems, delay decomposition approach, exponential stability


93D09, 93E03


  1. B. Boyd, L. E. Ghaoui, E. Feron and V. B. Balakrishnan: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia 1994.   CrossRef
  2. G. Chen and Y. Shen: Robust $H_\infty$ filter design for neutral stochastic uncertain systems with time-varying delay. J. Math. Anal. Appl. 353 (2009), 1, 196-204.   CrossRef
  3. W.-H. Chen, W.-X. Zheng and Y. Shen: Delay-dependent stochastic stability and $H_\infty$-control of uncertain neutral stochastic systems with time delay. IEEE Trans. Automat. Control 54 (2009), 7, 1660-1667.   CrossRef
  4. Y. Chen, W.-X. Zheng and A. Xue: A new result on stability analysis for stochastic neutral systems. Automatica 46 (2010), 12, 2100-2104.   CrossRef
  5. B. Du, J. Lam, Z. Shu and Z. Wang: A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components. IET-Control Theory Appl. 3 (2009), 4, 383-390.   CrossRef
  6. E. Fridman: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control Lett. 43 (2001), 4, 309-319.   CrossRef
  7. F. Gouaisbaut and D. Peaucelle: Delay-dependent stability analysis of linear time delay systems. In: Proc. IFAC Workshop Time Delay Syst. 2006, pp. 1-12.   CrossRef
  8. H. Gao, Z. Fei, J. Lam and B. Du: Further results on exponential estimates of markovian jump systems with mode-dependent time-varying delays. IEEE Trans. Automaat. Control 56 (2011), 1, 223-229.   CrossRef
  9. H. Gao and T. Chen: New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Automat. Control 52 (2007), 2, 328-334.   CrossRef
  10. K. Gu, V. Kharitonov and J. Chen: Stability of Time-delay Systems. Birkhauser, Boston 2003.   CrossRef
  11. L. Huang and X. Mao: Delay-dependent exponential stability of neutral stochastic delay systems. IEEE Trans. Automat. Control 54 (2009), 1, 147-152.   CrossRef
  12. Q.-L. Han: A discrete delay decomposition approach stability of linear retarded and neutral systems. Automatica 45 (2009), 2, 517-524.   CrossRef
  13. Y. He, M. Wu, J.-H. She and G.-P. Liu: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control Lett. 51 (2004), 1, 57-65.   CrossRef
  14. K. Jerzy: Stochastic controllability and minimum energy control of systems with multiple delays in control. Appl. Math. Comput. 206 (2008), 2, 704-715.   CrossRef
  15. K. Jerzy: Stochastic controllability of linear systems with state delays. Internat. J. Appl. Math. Comput. Sci. 17 (2007), 1, 5-13.   CrossRef
  16. X.-G. Li, X.-J. Zhu, A. Cela and A. Reama: Stability analysis of neutral systems with mixed delays. Automatica 44 (2008), 8, 2968-2972.   CrossRef
  17. H. F. Li and K. Q. Gu: Discretized Lyapunov-Krasovskii functional for coupled dif\-fe\-ren\-tial-difference equations with multiple delay channels. Automatica 46 (2010), 5, 902-909.   CrossRef
  18. X. Mao: Stochastic Differential Equations and Their Applications. Horwood Publication, Chichester 1997.   CrossRef
  19. L. G. Wu, Z. G. Feng and W.-X. Zheng: Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE Trans. Neural Netw. 21 (2010), 9, 1396-1407.   CrossRef
  20. Y. Wang, Z. Wang and J. Liang: On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach. IEEE Trans. Syst. Man Cybernet. B 40 (2010), 3, pp. 729-740.   CrossRef
  21. S. Xu, P. Shi, Y. Chu and Y. Zou: Robust stochastic stabilization and $H_\infty$ control of uncertain neutral stochastic time-delay systems. J. Math. Anal. Appl. 314 (2006), 1, 1-16.   CrossRef
  22. S. Zhu, Z. Li and C. Zhang: Delay decomposition approach to delay-dependent stability for singular time-delay systems. IET-Control Theory Appl. 4 (2010), 11, 2613-2620.   CrossRef
  23. S. Zhou and L. Zhou: Improved exponential stability criteria and stabilization of T-S model-based neutral systems. IET-Control Theory Appl. 4 (2010), 12, 2993-3002.   CrossRef