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Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

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Hanyong Shao, Jianrong Zhao and Dan Zhang, "Novel Stability Criteria for Sampled-Data Systems With Variable Sampling Periods," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 257-262, Jan. 2020. doi: 10.1109/JAS.2017.7510376
Citation: Hanyong Shao, Jianrong Zhao and Dan Zhang, "Novel Stability Criteria for Sampled-Data Systems With Variable Sampling Periods," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 257-262, Jan. 2020. doi: 10.1109/JAS.2017.7510376

Novel Stability Criteria for Sampled-Data Systems With Variable Sampling Periods

doi: 10.1109/JAS.2017.7510376

the National Natural Science Foundation of China 61374090

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  • This paper is concerned with a novel Lyapunov-like functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.


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  • [1]
    T. W. Chen and B. A. Francis, Optimal Sampled-Data Control Systems. London: Springer, 1995.
    X. F. Jiang, Q.-L. Han, S. R. Liu, and A. K. Xue, "A new $H_{\infty}$ stabilization criterion for networked control systems, " IEEE Trans. Automat. Contr., vol. 53, no. 4, pp. 1025-1032, May 2008.
    H. Shao and Z. Zhang, "Delay-dependent state feedback stabilization for a networked control model with two additive input delays, " Applied Mathematics and Computation, vol. 265, 748-758, Aug. 2015. doi: 10.1016/j.amc.2015.05.114
    D. Yue, Q.-L. Han, and J. Lam, "Network based robust $H_{\infty}$ control of systems with uncertainty, " Automatica, vol. 41, no. 6, pp. 999-1007, Jun. 2005.
    H. Shao, Q. L. Han, J. R. Zhao, and D. Zhang, "A separation method of transmission delays and data packet dropouts from a lumped input delay in the stability problem of networked control systems, " Int. J. Robust Nonlinear Control, vol. 27, no. 11, pp. 1963-1973, Jun. 2017.
    K. Liu and E. Fridman, "Networked-based stabilization via discontinuous Lyapunov functionals, " Int. J. Robust Nonlin. Control, vol. 22, no. 4, pp. 420-436, Mar. 2012. https://www.researchgate.net/publication/227727574_Networked-based_stabilization_via_discontinuous_Lyapunov_functionals
    H. Fujioka, "Stability analysis of systems with aperiodic sample-and-hold devices, " Automatica, vol. 45, no. 3, pp. 771-775, Mar. 2009. https://www.sciencedirect.com/science/article/pii/S0005109808005220
    Y. S. Suh, "Stability and stabilization of nonuniform sampling systems, " Automatica, vol. 44, no. 12, pp. 3222-3226, Dec. 2008. https://www.sciencedirect.com/science/article/pii/S0005109808003191
    Y. Oishi and H. Fujioka, "Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities, " Automatica, vol. 46, no. 8, pp. 1327-1333, Aug. 2010. https://www.sciencedirect.com/science/article/pii/S0005109810002128
    P. Naghshtabrizi, J. P. Hespanha, and A. R. Teel, "Exponential stability of impulsive systems with application to uncertain sampled-data systems, " Syst. Control Lett., vol. 57, no. 5, pp. 378-385, May 2008.
    L. S. Hu, J. Lam, Y. Y. Cao, and H. H. Shao, "A linear matrix inequality (LMI) approach to robust $H_2$ sampled-data control for linear uncertain systems, " IEEE Trans. Syst. Man Cybern. B Cybern., vol. 33, no. 1, pp. 149-155, Feb. 2003.
    X. L. Zhu and D. Yue, "Stability of sampled-data systems with application to networked control systems, " in Proc. 32nd Chinese Control Conf., Xi'an, China, 2013, pp. 6572-6577. https://www.researchgate.net/publication/286274846_Stability_of_sampled-data_systems_with_application_to_networked_control_systems
    E. Fridman, A. Seuret, and J. P. Richard, "Robust sampled-data stabilization of linear systems: An input delay approach, " Automatica, vol. 40, no. 8, pp. 1441-1446, Aug. 2004. https://www.sciencedirect.com/science/article/pii/S0005109804000913
    E. Fridman, "A refined input delay approach to sampled-data control, " Automatica, vol. 46, no. 2, pp. 421-427, Feb. 2010. https://www.sciencedirect.com/science/article/pii/S000510980900541X
    H. Y. Shao, "Improved delay-dependent stability criteria for systems with a delay varying in a range, " Automatica, vol. 44, no. 12, pp. 3215-3218, Dec. 2008. https://www.researchgate.net/publication/222282872_Improved_delay-dependent_stability_criteria_for_systems_with_a_delay_varying_in_a_range
    H. Y. Shao, "New delay-dependent stability criteria for systems with interval delay, " Automatica, vol. 45, no. 3, pp. 744-749, Mar. 2009. https://www.sciencedirect.com/science/article/pii/S0005109808004937
    K. Liu and E. Fridman, "Wirtinger's inequality and Lyapunov-based sampled-data stabilization, " Automatica, vol. 48, no. 1, pp. 102-108, Jan. 2012. https://www.sciencedirect.com/science/article/pii/S0005109811004699
    K. Gu, "An integral inequality in the stability problem of time-delay systems, " in Proc. 39th IEEE Conf. Decision and Control, Sydney, Australia, 2000, pp. 2805-2810. https://www.researchgate.net/publication/3892078_An_integral_inequality_in_the_stability_problem_of_time-delay_systems
    A. Seuret, "A novel stability analysis of linear systems under asynchronous samplings, " Automatica, vol. 48, no. 1, pp. 177-182, Jan. 2012. https://www.sciencedirect.com/science/article/pii/S0005109811004730
    A. Seuret and F. Gouaisbaut, "Wirtinger-based integral inequality: Application to time-delay systems, " Automatica, vol. 49, no. 9, pp. 2860-2866, Sep. 2013. doi: 10.1016/j.automatica.2013.05.030
    H. Y. Shao, Q. L. Han, Z. Q. Zhang, and X. L. Zhu, "Sampling-interval-dependent stability for sampled-data systems with state quantization, " Int. J. Robust Nonlin. Control, vol. 24, no. 17, pp. 2995-3008, Nov. 2014.
    H. Shao, L. Shao, and Z. Feng, "Novel stability results for aperiodic sampled-data systems, " J. Franklin Institute, vol. 356, no. 12, pp. 6525- 6537, Aug. 2019.
    C. K. Zhang, L. Jiang, Y. He, H. Wu, and M. Wu, "Stability analysis for control systems with aperiodically sampled data using an augmented Lyapunov functional method, " IET Control Theory Appl., vol. 7, no. 9, pp. 1219-1226, Jun. 2013.
    H. Y. Shao, J. Lam, and Z. G. Feng. "Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling, " Int. J. Syst. Sci., vol. 47, no. 12, pp. 2893-2900, Sep. 2016. doi: 10.1080/00207721.2015.1036475


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    • A Lyapunov-like functional approach is proposed.
    • The Lyapunov-like functional is time-dependent.
    • The Lyapunov-like functional may be discontinuous.
    • The Lyapunov-like functional is not required to be positive definite.
    • The Lyapunov-like functional approach leads to less conservative stability results.


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