A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Nezar M. Alyazidi and Magdi S. Mahmoud, "Distributed \begin{document}$H_{2}/H_\infty$\end{document} Filter Design for Discrete-Time Switched Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 158-168, Jan. 2020. doi: 10.1109/JAS.2019.1911630
Citation: Nezar M. Alyazidi and Magdi S. Mahmoud, "Distributed \begin{document}$H_{2}/H_\infty$\end{document} Filter Design for Discrete-Time Switched Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 158-168, Jan. 2020. doi: 10.1109/JAS.2019.1911630

Distributed $H_{2}/H_\infty$ Filter Design for Discrete-Time Switched Systems

doi: 10.1109/JAS.2019.1911630

the Deanship of Scientific Research (DSR) at KFUPM through distinguished professorship project 161065

More Information
  • This paper addresses an infinite horizon distributed $\pmb{H}_{\bf 2}/\pmb{H}_{\bf\infty}$ filtering for discrete-time systems under conditions of bounded power and white stochastic signals. The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling. Herein, we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed $\pmb H_{\bf 2}$ and $\pmb{H_{\bf\infty}}$ schemes over a finite horizon. A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances. It is shown that the stability of the overall filtering-error system with $\pmb{H}_{\bf 2}/\pmb{H}_{\bf\infty}$ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed. A simulation example is given to show the effectiveness of the proposed approach.


  • loading
  • Recommended by Associate Editor Mohammed Chadli.
  • [1]
    M. S. Mahmoud, "Distributed estimation based on information-based covariance intersection algorithms", Int. J. Adapt. Control Signal Process, vol. 30, pp.750-778, 2015. https://www.researchgate.net/publication/283958509_Distributed_estimation_based_on_information-based_covariance_intersection_algorithms
    R. S. Olfati, "Kalman-consensus filter: optimality, stability, and performance" in Proc. 28th Chinese Decision and Control Conf., pp. 7036-7042, 2009. https://www.researchgate.net/publication/224108550_Kalman-Consensus_Filter_Optimality_Stability_and_Performance
    F. S. Cattivelli and A.H. Sayed, "Diffusion strategies for distributed Kalman filtering and smoothing, " IEEE Trans. Automatic Control, vol. 55, no. 9, pp. 2069-2084, 2010. doi: 10.1109/TAC.2010.2042987
    M. S. Mahmoud, L. H. Xie, and C. Y. Soh, "Robust Kalman filtering for discrete state-delay systems", in Proc. IEEE Control Theory and Applications, vol. 147, no. 6, pp. 613-618, 2000. https://www.researchgate.net/publication/3352360_Robust_Kalman_filtering_for_discrete_state-delay_systems
    M. S. Mahmou and H. M. Khalid, "Distributed Kalman filtering: a bibliographic review, " IET Control Theory and Applications, vol. 7, no. 4, pp.483-501, 2013. doi: 10.1049/iet-cta.2012.0732
    Y. Zhu, Z. You, J. Zhao, K. Zhang, and R. X. Li, "The optimality for the distributed Kalman filtering fusion", Automatica, vol. 37, no. 9, pp. 1489-1493, 2001. doi: 10.1016/S0005-1098(01)00074-7
    I. Petersen and A. Savkin, "Robust Kalman filtering for signals and systems with large uncertainties, " Control Engineering, 2013.
    J. Hu, L. Xie, and C. Zhang, "Diffusion Kalman filtering based on covariance intersection, " IEEE Trans. Signal Processing, vol. 60, no. 2, pp. 891-902, 2012. doi: 10.1109/TSP.2011.2175386
    B. Shen, Z. Wang, and Y. Hung, "Distributed-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case, " Automatica, vol. 46, no. 10, pp. 1682-1688, 2010. doi: 10.1016/j.automatica.2010.06.025
    V. Ugrinovskii, "Distributed robust filtering with consensus of estimates, " Automatica, vol. 47, no. 1, pp. 1-13, 2011. doi: 10.1016/j.automatica.2010.10.002
    V. Ugrinovskii, "Distributed robust estimation over randomly switching networks using consensus, " Automatica, vol. 49, no. 1, pp. 160-168, 2013. doi: 10.1016/j.automatica.2012.09.010
    T. Jiang, I. Matei, and J. S. Baras, "A trust-based distributed Kalman filtering approach for mode estimation in power systems", in Proc. 1st Workshop Secure Control Systems (SCS), pp. 1-6, April 12, 2010.
    S. R. Olfati, "Distributed Kalman filtering for sensor networks." in Proc. IEEE 46th Conf. Decision and Control, pp. 5492-5498, 2007. https://www.researchgate.net/publication/224303218_Distributed_Kalman_filtering_for_sensor_networks
    C. Jiang, Y. Chen, and K. R. Liu, "Distributed adaptive networks: a graphical evolutionary game-theoretic view, " IEEE Trans. Signal Processing, vol. 61, no. 22, pp.5675-5688, 2013. doi: 10.1109/TSP.2013.2280444
    K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, New Jersey: Prentice hall, vol. 40, 1996. http://d.old.wanfangdata.com.cn/Periodical/zdhxb200301010
    B. D. Anderson and J. B. Moore, "Optimal control: linear quadratic methods, " Courier Corporation, Feb. 27, 2007. https://www.researchgate.net/publication/260228778_Optimal_Control_Linear_Quadratic_Method
    C. Olalla, R. Leyva, A. El Aroudi, and I. Queinnec, "Robust LQR control for PWM converters: an LMI approach, " IEEE Trans. Industrial Electronics, vol. 56, no. 7, pp. 2548-2558, 2009. doi: 10.1109/TIE.2009.2017556
    B. S. Chen and W. Zhang, "Stochastic $H_{2}/H_\infty$ control with state-dependent noise, " IEEE Trans. Automatic Control, vol. 49, no. 1, pp. 45-57, 2004. doi: 10.1109/TAC.2003.821400
    W. Zhang, Y. Huang, and H. Zhang, "Stochastic $H_{2}/H_\infty$ control for discrete-time systems with state and disturbance dependent noise, " Automatica, vol.43, no. 3, pp. 513-521, 2007. doi: 10.1016/j.automatica.2006.09.015
    D. Bernstein and M. Haddad, "LQG control with an $H_\infty$ performance bound: a Riccati equation approach, " IEEE Trans. Automatic Control, vol. 34, no. 3, pp. 293-305, 1989. doi: 10.1109/9.16419
    C. S. Tseng and B. S. Chen, "A mixed $H_{2}/H_\infty$ adaptive tracking control for constrained non-holonomic systems, " Automatica, vol. 39, no. 6, pp. 1011-1018, 2003. doi: 10.1016/S0005-1098(03)00038-4
    C. Chen, W. Dong and V. Djapic, " Distributed $H_{2}/H_\infty$ filtering over infinite horizon, " Int. J. Adaptive Control and Signal Processing, vol. 32, no. 2, pp. 330-343, 2018. doi: 10.1002/acs.2847
    M. S. Mahmoud, Switched Time-Delay Systems: Stability and Control, Boston: Springer, pp. 109-130, 2010. http://d.old.wanfangdata.com.cn/Periodical/xtgcydzjs201001033
    F. L. Lewis and V. L. Syrmos, Optimal Control, John Wiley & Sons, 1995. http://d.old.wanfangdata.com.cn/Periodical/lxxb201606015
    N. M. Alyazidi, M. S. Mahmoud, and M. I. Abouheaf, "Adaptive critics based cooperative control scheme for islanded microgrids, " Neurocomputing, vol. 272, pp.532-541, 2018. doi: 10.1016/j.neucom.2017.07.027


    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


    Article Metrics

    Article views (1118) PDF downloads(48) Cited by()


    • It provides complete results of the infinite horizon distributed H2/Hoo filtering design problem for discrete-time systems with bounded power stochastic signals.
    • Essentially, it formulates the filtering design solution as a two-step procedure, which aims at lessening the computational load.
    • To guarantee the stability of the system, a switched strategy developed by switching the state according to the change in the operation conditions.
    • The performance evaluation of the filter under external disturbances are demonstrated.


    DownLoad:  Full-Size Img  PowerPoint