Volume 12 Number 6
December 2015
Article Contents
Tuo Zhou and Xi-Qin He. An Improved H∞ Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay. International Journal of Automation and Computing, vol. 12, no. 6, pp. 671-678, 2015. doi: 10.1007/s11633-015-0930-x
Cite as: Tuo Zhou and Xi-Qin He. An Improved H∞ Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay. International Journal of Automation and Computing, vol. 12, no. 6, pp. 671-678, 2015. doi: 10.1007/s11633-015-0930-x

An Improved H Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay

  • Received: 2014-08-27
Fund Project:

This work was supported in part by Funds of National Science of China (No. 61174215).

  • This paper addresses a robust H filter design problem for nonlinear systems with time-varying delay through Takagi-Sugeno (T-S) fuzzy model approach. Firstly, by introducing free-weighting matrix method combined with a matrix decoupling approach and adopting an improved integral inequality method without ignoring any integral term, less conservative results are achieved. Next, based on the model, new delay-dependent sufficient conditions are derived, which are less conservative than the existing ones via solving the linear matrix inequalities (LMIs). Lastly, simulations show a significant improvement over the previous results.
  • [1] R. E. Kalman. A new approach to linear filtering and prediction problems. Journal of Fluids Engineering, vol. 82, no. 1, pp. 35-45, 1960.
    [2] A. Elsayed, M. J. Grimble. A new approach to the H design of optimal digital linear filters. IMA Journal of Mathematical Control and Information, vol. 6, no. 2, pp. 233-251, 1989.
    [3] L. H. Xie, C. E. de Souza, M. Y. Fu. H estimation for discrete-time linear uncertain systems. International Journal of Robust and Nonlinear Control, vol. 1, no. 2, pp. 111-123, 1991.
    [4] M. Basin, E. Sanchez, R. Martinez-Zuniga. Optimal linear filtering for systems with multiple state and observation delays. International Journal of Innovative Computing, Information and Control, vol. 3, no. 5, pp. 1309-1320, 2007.
    [5] H. J. Gao, C. H. Wang. A delay-dependent approach to robust H filtering for uncertain discrete-time state-delayed systems. IEEE Transactions on Signal Processing, vol. 52, no. 6, pp. 1631-1640, 2004.
    [6] H. J. Gao, J. Lam, L. H. Xie, C. H. Wang. New approach to mixed H2/H filtering for polytopic discretetime systems. IEEE Transactions on Signal Processing, vol. 53, no. 8, pp. 3183-3192, 2005.
    [7] X. M. Zhang, Q. L. Han. Robust H filtering for a class of uncertain linear systems with time-varying delay. Automatica, vol. 44, no. 1, pp. 157-166, 2008.
    [8] J. Sun, J. Chen, G. P. Liu, D. Rees. Delay-dependent robust H filter design for uncertain linear systems with time-varying delay. Circuits, Systems & Signal Processing, vol. 28, no. 5, pp. 763-779, 2009.
    [9] G. P. Liu, Y. Q. Xia, D. Rees, W. S. Hu. Design and stability criteria of networked predictive control systems with random network delay in the feedback channel. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 37, no. 2, pp. 173-184, 2007.
    [10] D. Yue, Q. L. Han, J. Lam. Network-based robust H control of systems with uncertainty. Automatica, vol. 41, no. 6, pp. 999-1007, 2005.
    [11] C. Gong, B. K. Su. Robust L2-L filtering of convex polyhedral uncertain time-delay fuzzy systems. International Journal of Innovative Computing, Information and Control, vol. 4, no. 4, pp. 793-802, 2008.
    [12] C. L. Zhang, J.M. Li. Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network. International Journal of Automation and Computing, vol. 8, no. 4, pp. 403-410, 2011.
    [13] D. Zhang, Q. G. Wang, L. Yu, Q. K. Shao. H filtering for networked systems with multiple time-varying transmissions and random packet dropouts. IEEE Transactions on Industrial Informatics, vol. 9, no. 3, pp. 1705-1716, 2013.
    [14] M. S. Mahmoud. Resilient L2-L filtering of polytopic systems with state delays. IET Control Theory & Applications, vol. 1, no. 1, pp. 141-154, 2007.
    [15] Z. D.Wang, B. Huang, H. Unbehauen. Robust H observer design of linear time-delay systems with parametric uncertainty. Systems & Control Letters, vol. 42, no. 4, pp. 303-312, 2001.
    [16] Z. D. Wang, D. P. Goodall, K. J. Burnham. On designing observers for time-delay systems with non-linear disturbances. International Journal of Control, vol. 75, no. 11, pp. 803-811, 2002.
    [17] S. Y. Xu, T. W. Chen. An LMI approach to the H filter design for uncertain systems with distributed delays. IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 51, no. 4, pp. 195-201, 2004.
    [18] S. Y. Xu, J. Lam, T. W. Chen, Y. Zou. A delay-dependent approach to robust H filtering for uncertain distributed delay systems. IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3764-3772, 2005.
    [19] A. Pila, U. Shaked, C. de Souza. H filtering for continuous-time linear systems with delay. IEEE Transactions on Automatic Control, vol. 44, no. 7, pp. 1412-1417, 1999.
    [20] C. E. de Souza, R. M. Palhares, P. L. D. Peres. Robust H filter design for uncertain linear systems with multiple time-varying state delays. IEEE Transactions on Signal Processing, vol. 49, no. 3, pp. 569-576, 2001.
    [21] X. H. Ge, Q. L. Han, X. F. Jiang. Sampled-data H filtering of Takagi-Sugeno fuzzy systems with interval timevarying delays. Journal of the Franklin Institute, vol. 351, no. 5, pp. 2515-2542, 2014.
    [22] J. H. Zhang, Y. Q. Xiao, R. Tao. New results on H filtering for fuzzy time-delay systems. IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 128-137, 2009.
    [23] W. G. Yu, Z. Gu, S. L. Hu. H filtering for time-delay systems with Markovian jumping parameters: Delay partitioning approach. Journal of the Chinese Institute of Engineers, vol. 33, no. 3, pp. 357-365, 2010.
    [24] P. Wang, W. W. Sun. Adaptive H control for nonlinear Hamiltonian systems with time delay and parametric uncertainties. International Journal of Automation and Computing, vol. 11, no. 4, pp. 368-376, 2014.
    [25] X. M. Zhang, Q. L. Han. Novel delay-derivative-dependent stability criteria using new bounding techniques. International Journal of Robust and Nonlinear Control, vol. 23, no. 13, pp. 1419-1432, 2013.
    [26] X. M. Zhang, Q. L. Han. New stability criterion using a matrix-based quadratic convex approach and some novel integral inequalities. IET Control Theory & Applications, vol. 8, no. 12, pp. 1054-1061, 2014.
    [27] T. Takagi, M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116-132, 1985.
    [28] C. Lin, G. Q.Wang, T. H. Lee, B. Chen. H filter design for nonlinear systems with time-delay through T-S fuzzy model approach. IEEE Transactions on Fuzzy Systems, vol. 16, no. 3, pp. 739-746, 2008.
    [29] Y. K. Su, B. Chen, C. Lin, H. G. Zhang. A new fuzzy H filter design for nonlinear continuous-time dynamic systems with time-varying delays. Fuzzy Sets and Systems, vol. 160, no. 24, pp. 3539-3549, 2009.
    [30] J. H. Zhang, Y. Q. Xiao, R. Tao. New results on H filtering for fuzzy time-delay systems. IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 128-137, 2009.
    [31] S. J. Huang, X. Q. He, N. N. Zhang. New results on H filter design for nonlinear systems with time delay via T-S fuzzy models. IEEE Transactions on Fuzzy Systems, vol. 19, no. 1, pp. 193-199, 2011.
    [32] S. J. Huang, G. H. Yang. Fault tolerant controller design for T-S fuzzy systems with time-varying delay and actuator faults: A k-step fault-estimation approach. IEEE Transactions on Fuzzy Systems, vol. 22, no. 6, pp. 1526-1540, 2014.
    [33] X. F. Jiang, Q. L. Han. On designing fuzzy controllers for a class of nonlinear networked control systems. IEEE Transactions on Fuzzy Systems, vol. 16, no. 4, pp. 1050-1060, 2008.
    [34] X. F. Jiang, Q. L. Han. New stability criteria for linear systems with interval time-varying delay. Automatica, vol. 44, no. 10, pp. 2680-2685, 2008.
    [35] X. F. Jiang, Q. L. Han, S. R. Liu, A. K. Xue. A new H stabilization criterion for networked control systems. IEEE Transactions on Automatic Control, vol. 53, no. 4, pp. 1025-1032, 2008.
    [36] X. F. Jiang, Q. L. Han. Delay-dependent H filter design for linear systems with interval time-varying delay. IET Control Theory & Applications, vol. 1, no. 4, pp. 1131-1140, 2007.
  • 加载中
  • [1] Jun-Jun Hui,  He-Xin Zhang,  Xiang-Yu Kong,  Xin Zhou. On Improved Delay-dependent Robust Stability Criteria for Uncertain Systems with Interval Time-varying Delay . International Journal of Automation and Computing, 2015, 12(1): 102-108.  doi: 10.1007/s11633-014-0822-5
    [2] Jun-Jun Hui,  He-Xin Zhang,  Xiang-Yu Kong. Delay-dependent Non-fragile H Control for Linear Systems with Interval Time-varying Delay . International Journal of Automation and Computing, 2015, 12(1): 109-116.  doi: 10.1007/s11633-014-0851-0
    [3] Alessandro di Gaeta,  Umberto Montanaro. Application of a Robust Model Reference Adaptive Control Algorithm to a Nonlinear Automotive Actuator . International Journal of Automation and Computing, 2014, 11(4): 377-391.  doi: 10.1007/s11633-014-0803-8
    [4] A Stability Criterion for Singular Systems with Two Additive Time-varying Delay Components . International Journal of Automation and Computing, 2013, 10(1): 39-45 .  doi: 10.1007/s11633-013-0694-0
    [5] Meng Zhao,  Bao-Cang Ding. A Contractive Sliding-mode MPC Algorithm for Nonlinear Discrete-time Systems . International Journal of Automation and Computing, 2013, 10(2): 167-172.  doi: 10.1007/s11633-013-0709-x
    [6] Imen Haj Brahim, Maha Bouattour, Driss Mehdi, Mohamed Chaabane, Ghani Hashim. Sensor Faults Observer Design with H Performance for Non-linear T-S systems . International Journal of Automation and Computing, 2013, 10(6): 563-570.  doi: 10.1007/s11633-013-0754-5
    [7] P. Balasubramaniam,  T. Senthilkumar. Delay-dependent Robust Stabilization and H Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delay . International Journal of Automation and Computing, 2013, 10(1): 18-31 .  doi: 10.1007/s11633-013-0692-2
    [8] Hassan A. Yousef, Mohamed Hamdy. Observer-based Adaptive Fuzzy Control for a Class of Nonlinear Time-delay Systems . International Journal of Automation and Computing, 2013, 10(4): 275-280.  doi: 10.1007/s11633-013-0721-1
    [9] Xiao-Cheng Shi,  Tian-Ping Zhang. Adaptive Tracking Control of Uncertain MIMO Nonlinear Systems with Time-varying Delays and Unmodeled Dynamics . International Journal of Automation and Computing, 2013, 10(3): 194-201.  doi: 10.1007/s11633-013-0712-2
    [10] Zhong-Cai Zhang,  Yu-Qiang Wu. Globally Asymptotic Stabilization for Nonlinear Time-delay Systems with ISS Inverse Dynamics . International Journal of Automation and Computing, 2012, 9(6): 634-640 .  doi: 10.1007/s11633-012-0689-2
    [11] Chang-Liang Liu, Shao-Cheng Tong, Yong-Ming Li, Yuan-Qing Xia. Adaptive Fuzzy Backstepping Output Feedback Control of Nonlinear Time-delay Systems with Unknown High-frequency Gain Sign . International Journal of Automation and Computing, 2011, 8(1): 14-22.  doi: 10.1007/s11633-010-0549-x
    [12] Xian-Ming Tang,  Jin-Shou Yu. Stability Analysis of Discrete-time Systems with Additive Time-varying Delays . International Journal of Automation and Computing, 2010, 7(2): 219-223.  doi: 10.1007/s11633-010-0219-z
    [13] Xu-Dong Zhao,  Qing-Shuang Zeng. H Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters . International Journal of Automation and Computing, 2010, 7(4): 447-454.  doi: 10.1007/s11633-010-0526-4
    [14] Wei-Sheng Chen,  Rui-Hong Li,  Jing Li. Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays . International Journal of Automation and Computing, 2010, 7(4): 438-446.  doi: 10.1007/s11633-010-0525-5
    [15] Shao-Cheng Tong,  Yong-Ming Li. Adaptive Backstepping Output Feedback Control for SISO Nonlinear System Using Fuzzy Neural Networks . International Journal of Automation and Computing, 2009, 6(2): 145-153.  doi: 10.1007/s11633-009-0145-0
    [16] Fatima El Haoussi,  El Houssaine Tissir. Robust H Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback . International Journal of Automation and Computing, 2009, 6(2): 164-170.  doi: 10.1007/s11633-009-0164-x
    [17] Ying Zhang, Ai-Guo Wu, Guang-Ren Duan. Enhanced H Filtering for Continuous-time State-delayed Systems . International Journal of Automation and Computing, 2009, 6(2): 159-163.  doi: 10.1007/s11633-009-0159-7
    [18] Guang-Deng Zong,  Jia Liu. New Delay-dependent Global Asymptotic Stability Condition for Hopfield Neural Networks with Time-varying Delays . International Journal of Automation and Computing, 2009, 6(4): 415-419.  doi: 10.1007/s11633-009-0415-x
    [19] Xiao-Bing Hu, Wen-Hua Chen. Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control . International Journal of Automation and Computing, 2007, 4(2): 195-202.  doi: 10.1007/s11633-007-0195-0
    [20] Sing Kiong Nguang, Ping Zhang, Steven X. Ding. Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach . International Journal of Automation and Computing, 2007, 4(2): 164-168.  doi: 10.1007/s11633-007-0164-7
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Abstract Views (4413) PDF downloads (1153) Citations (0)

An Improved H Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay

Fund Project:

This work was supported in part by Funds of National Science of China (No. 61174215).

Abstract: This paper addresses a robust H filter design problem for nonlinear systems with time-varying delay through Takagi-Sugeno (T-S) fuzzy model approach. Firstly, by introducing free-weighting matrix method combined with a matrix decoupling approach and adopting an improved integral inequality method without ignoring any integral term, less conservative results are achieved. Next, based on the model, new delay-dependent sufficient conditions are derived, which are less conservative than the existing ones via solving the linear matrix inequalities (LMIs). Lastly, simulations show a significant improvement over the previous results.

Tuo Zhou and Xi-Qin He. An Improved H∞ Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay. International Journal of Automation and Computing, vol. 12, no. 6, pp. 671-678, 2015. doi: 10.1007/s11633-015-0930-x
Citation: Tuo Zhou and Xi-Qin He. An Improved H∞ Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay. International Journal of Automation and Computing, vol. 12, no. 6, pp. 671-678, 2015. doi: 10.1007/s11633-015-0930-x
Reference (36)

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return