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SCIENCE CHINA Information Sciences, Volume 59, Issue 3: 032204(2016) https://doi.org/10.1007/s11432-015-5386-7

Robust $H_2/H_{\infty}$ global linearization filter design for nonlinear stochastic time-varying delay systems Robust $H_2/H_{\infty}$ global linearization filter design for nonlinear stochastic time-varying delay systems

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  • ReceivedJan 12, 2015
  • AcceptedApr 8, 2015
  • PublishedJan 22, 2016

Abstract

One can design a robust $H_{\infty}$ filter for a general nonlinear stochastic system with external disturbance by solving a second-order nonlinear stochastic partial Hamilton-Jacobi inequality (HJI), which is difficult to be solved. in this paper, the robust mixed $H_2/H_{\infty}$ globally linearized filter design problem is investigated for a general nonlinear stochastic time-varying delay system with external disturbance, where the state is governed by a stochastic It${\rm \hat{o}}$-type equation. based on a globally linearized model, a stochastic bounded real lemma is established by the Lyapunov--Krasovskii functional theory, {and} the robust $H_{\infty}$ globally linearized filter is designed by solving the simultaneous linear matrix inequalities instead of solving an HJI. for a given attenuation level, the $H_2$ globally linearized filtering problem with the worst case disturbance in the $H_\infty$ filter case is known as the mixed $H_2/H_{\infty}$ globally linearized filtering problem, which can be formulated as a linear programming problem with simultaneous LMI constraints. Therefore, this method is applicable for state estimation in nonlinear stochastic time-varying delay systems with unknown exogenous disturbance when state variables are unavailable. A simulation example is provided to illustrate the effectiveness of the proposed method.


Funded by

{} Fundamental Research Funds for the Central Universities(13lgpy31)

National Natural Science Foundation of China(61273126)

National Natural Science Foundation of China(11201495)

Natural Science Foundation of Guangdong Province(2015A030310065)


Acknowledgment

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 61273126, 11201495), Natural Science Foundation of Guangdong Province (Grant No. 2015A030310065){, and} Fundamental Research Funds for the Central Universities (Grant No. 13lgpy31).


References

[1] Xu S Y, Lam J, Mao X R. IEEE Trans Circuits Syst I, Reg Papers, 2007, 54: 2070-2077 Google Scholar

[2] Chen B S, Tsai C L, Chen Y F. IEEE Trans Signal Process, 2001, 49: 2693-2701 CrossRef Google Scholar

[3] Nagpal K M, Khargonekar P P. IEEE Trans Autom Control, 1991, 36: 152-166 CrossRef Google Scholar

[4] Xu S Y, Chen T. IEEE Trans Signal Process, 2002, 50: 2998-3007 CrossRef Google Scholar

[5] Chen G C, Shen Y. J Math Anal Appl, 2009, 353: 196-204 CrossRef Google Scholar

[6] Song B, Xu S Y, Xia J W, et al. Asian J Control, 2010, 12: 39-45 Google Scholar

[7] Wu H N, Luo B. IEEE Trans Neural Netw Learn Syst, 2012, 23: 1884-1895 CrossRef Google Scholar

[8] Luo B, Wu H N. Int J Robust Nonlin Control, 2013, 23: 991-1012 CrossRef Google Scholar

[9] Liu Y G, Zhang J F, Pan Z G. Sci China Ser F-Inf Sci, 2003, 46: 126-144 CrossRef Google Scholar

[10] Zhang W H, Feng G. IEEE Trans Autom Control, 2008, 53: 1323-1328 CrossRef Google Scholar

[11] Zhang W H, Chen B S, Tang H B, et al. IEEE Trans Autom Control, 2014, 59: 237-242 CrossRef Google Scholar

[12] Wu A G, Liu X N, Zhang Y. Asian J of Control, 2012, 14: 1676-1682 CrossRef Google Scholar

[13] Abbaszadeh M, Marquez H J. J Control Theory Appl, 2012, 10: 152-158 CrossRef Google Scholar

[14] Zhang W H, Chen B S, Tseng C S. IEEE Trans Signal Process, 2005, 53: 589-598 CrossRef Google Scholar

[15] Chen B S, Chen W H, Wu H L. IEEE Trans Circuits Syst I, Reg Papers, 2009, 56: 1441-1454 Google Scholar

[16] Tseng C S. IEEE Trans Fuzzy Syst, 2007, 15: 261-274 CrossRef Google Scholar

[17] Chen W H, Chen B S. Fuzzy Sets Syst, 2013, 217: 41-61 CrossRef Google Scholar

[18] Calzolari A, Florchinger P, Nappo G. Comput Math Appl, 2011, 61: 2498-2509 CrossRef Google Scholar

[19] Zhang W H, Feng G, Li Q H. Math Probl Eng, 2012, 2012: 231352-2509 Google Scholar

[20] Yan H C, Zhang H, Shi H B, et al. Circuits Syst Signal Process, 2011, 30: 303-321 CrossRef Google Scholar

[21] Shen B, Wang Z D, Hung Y S. IEEE Trans Ind Electron, 2011, 58: 1971-1979 CrossRef Google Scholar

[22] Li H P, Shi Y. Automatica, 2012, 48: 159-166 CrossRef Google Scholar

[23] Wang Z D, Huang B. IEEE Trans Signal Process, 2000, 48: 2463-2467 CrossRef Google Scholar

[24] Gao H J, Lam J, Xie L H, et al. IEEE Trans Signal Process, 2005, 53: 3183-3192 CrossRef Google Scholar

[25] Qiu J Q, Feng G, Yang J. IEEE Trans Circuits Syst II, Exp Briefs, 2008, 55: 178-182 Google Scholar

[26] Velni J M, Grigoriadis K M. IEEE Trans Circuits Syst I, Reg Papers, 2008, 55: 2097-3105 Google Scholar

[27] Chen B S, Zhang W H, Chen Y Y. On the robust state estimation of nonlinear stochastic systems with state-dependent noise. In: Proceedings of the 2002 International Conference on Control and Automation, Xiamen, 2002. 2299--2304. Google Scholar

[28] Hinrichsen D, Pritchard A J. SIAM J Control Optim, 1998, 36: 1504-1538 CrossRef Google Scholar

[29] Chen B S, Zhang W H. SIAM J Control Optim, 2006, 44: 1973-1991 CrossRef Google Scholar

[30] Chen P N, Qin H S, Wang Y, et al. Sci China Inf Sci, 2012, 55: 200-213 CrossRef Google Scholar

[31] Yang R M, Wang Y Z. Sci China Inf Sci, 2012, 55: 1218-1228 CrossRef Google Scholar

[32] Li C Y, Guo L. Sci China Inf Sci, 2013, 56: 012201-1228 Google Scholar

[33] Wang Y Z, Feng G. Sci China Inf Sci, 2013, 56: 108202-1228 Google Scholar

[34] Boyd S, Ghaoui L El, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994. 51--60. Google Scholar

[35] Luo Q, Mao X R, Shen Y. Automatica, 2011, 47: 2075-2081 CrossRef Google Scholar

[36] Mao X R. Stochastic Differential Equations and Applications. 2nd ed. Chichester: Horwood, 2007. 112--114. Google Scholar

[37] Berman N, Shaked U. $H_{\infty}$ for nonlinear stochastic systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, 2003. 5025--5030. Google Scholar

[38] Gu K, Kharitonov V L, Chen J. Stability of Time-Delay Systems. Berlin: Springer, 2003. 316. Google Scholar

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