# Article

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Keywords:
neutral stochastic time-delay systems; delay decomposition approach; exponential stability; linear matrix inequality (LMI)
Summary:
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.
References:
[1] Boyd, B., Ghaoui, L. E., Feron, E., Balakrishnan, V. B.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia 1994. MR 1284712
[2] Chen, G., Shen, Y.: Robust $H_\infty$ filter design for neutral stochastic uncertain systems with time-varying delay. J. Math. Anal. Appl. 353 (2009), 1, 196-204. DOI 10.1016/j.jmaa.2008.11.062 | MR 2508857 | Zbl 1161.93025
[3] Chen, W.-H., Zheng, W.-X., Shen, Y.: 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. DOI 10.1109/TAC.2009.2017981 | MR 2535767
[4] Chen, Y., Zheng, W.-X., Xue, A.: A new result on stability analysis for stochastic neutral systems. Automatica 46 (2010), 12, 2100-2104. DOI 10.1016/j.automatica.2010.08.007 | MR 2878237 | Zbl 1205.93160
[5] Du, B., Lam, J., Shu, Z., Wang, Z.: A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components. IET-Control Theory Appl. 3 (2009), 4, 383-390. MR 2512656
[6] Fridman, E.: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control Lett. 43 (2001), 4, 309-319. DOI 10.1016/S0167-6911(01)00114-1 | MR 2008812 | Zbl 0974.93028
[7] Gouaisbaut, F., Peaucelle, D.: Delay-dependent stability analysis of linear time delay systems. In: Proc. IFAC Workshop Time Delay Syst. 2006, pp. 1-12.
[8] Gao, H., Fei, Z., Lam, J., Du, B.: Further results on exponential estimates of markovian jump systems with mode-dependent time-varying delays. IEEE Trans. Automaat. Control 56 (2011), 1, 223-229. DOI 10.1109/TAC.2010.2090575 | MR 2777223
[9] Gao, H., Chen, T.: New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Automat. Control 52 (2007), 2, 328-334. DOI 10.1109/TAC.2006.890320 | MR 2295017
[10] Gu, K., Kharitonov, V., Chen, J.: Stability of Time-delay Systems. Birkhauser, Boston 2003. Zbl 1039.34067
[11] Huang, L., Mao, X.: Delay-dependent exponential stability of neutral stochastic delay systems. IEEE Trans. Automat. Control 54 (2009), 1, 147-152. DOI 10.1109/TAC.2008.2007178 | MR 2478078
[12] Han, Q.-L.: A discrete delay decomposition approach stability of linear retarded and neutral systems. Automatica 45 (2009), 2, 517-524. DOI 10.1016/j.automatica.2008.08.005 | MR 2527352
[13] He, Y., Wu, M., She, J.-H., Liu, G.-P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control Lett. 51 (2004), 1, 57-65. DOI 10.1016/S0167-6911(03)00207-X | MR 2026262 | Zbl 1157.93467
[14] Jerzy, K.: Stochastic controllability and minimum energy control of systems with multiple delays in control. Appl. Math. Comput. 206 (2008), 2, 704-715. DOI 10.1016/j.amc.2008.08.059 | MR 2483043 | Zbl 1167.93008
[15] Jerzy, K.: Stochastic controllability of linear systems with state delays. Internat. J. Appl. Math. Comput. Sci. 17 (2007), 1, 5-13. MR 2310791 | Zbl 1133.93307
[16] Li, X.-G., Zhu, X.-J., Cela, A., Reama, A.: Stability analysis of neutral systems with mixed delays. Automatica 44 (2008), 8, 2968-2972. MR 2527226 | Zbl 1152.93450
[17] Li, H. F., Gu, K. Q.: Discretized Lyapunov-Krasovskii functional for coupled differential-difference equations with multiple delay channels. Automatica 46 (2010), 5, 902-909. DOI 10.1016/j.automatica.2010.02.007 | MR 2877164 | Zbl 1191.93120
[18] Mao, X.: Stochastic Differential Equations and Their Applications. Horwood Publication, Chichester 1997. MR 1475218 | Zbl 0892.60057
[19] Wu, L. G., Feng, Z. G., Zheng, W.-X.: Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE Trans. Neural Netw. 21 (2010), 9, 1396-1407. DOI 10.1109/TNN.2010.2056383
[20] Wang, Y., Wang, Z., Liang, J.: 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. DOI 10.1109/TSMCB.2009.2026059
[21] Xu, S., Shi, P., Chu, Y., Zou, Y.: Robust stochastic stabilization and $H_\infty$ control of uncertain neutral stochastic time-delay systems. J. Math. Anal. Appl. 314 (2006), 1, 1-16. DOI 10.1016/j.jmaa.2005.03.088 | MR 2183533 | Zbl 1127.93053
[22] Zhu, S., Li, Z., Zhang, C.: Delay decomposition approach to delay-dependent stability for singular time-delay systems. IET-Control Theory Appl. 4 (2010), 11, 2613-2620. MR 2798844
[23] Zhou, S., Zhou, L.: Improved exponential stability criteria and stabilization of T-S model-based neutral systems. IET-Control Theory Appl. 4 (2010), 12, 2993-3002. MR 2808635

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