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Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator

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Abstract

The quantized output feedback stabilization problem for nonlinear discrete-time systems with saturating actuator is investigated. The nonlinearity is assumed to satisfy the local Lipschitz condition. Different from the previous results where the Lipschitz constant is predetermined, a more general case is considered, where the maximum admissible Lipschitz constant through convex optimization is obtained. In this framework, two kinds of quantizations are derived simultaneously: quantized control input and quantized output. Furthermore, sufficient conditions for the existence of static output feedback control laws are given. The desired controllers ensure that all the trajectories of the closed-loop system will converge to a minimal ellipsoid for every initial condition emanating from a large admissible domain. Finally, four illustrative examples are provided to show the effectiveness of the proposed approach.

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References

  1. Liberzon, D.: Hybrid feedback stabilization of systems with quantized signals. Automatica 39, 1543–1554 (2003)

  2. Ishii, H., Francis, B.A.: Quadratic stabilization of sampled-data systems with quantization. Automatica 39, 1793–1800 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang, C., Feng, G., Qiu, J., Shen, Y.: Control synthesis for a class of linear network-based systems with communication constraints. IEEE Trans. Ind. Electron. 60, 3339–3348 (2013)

    Google Scholar 

  4. Mahmoud, M., Al-Rayyah, A., Xia, Y.: Quantised feedback stabilisation of interconnected discrete-delay systems. IET Control Theory Appl. 5, 795–802 (2011)

    Article  MathSciNet  Google Scholar 

  5. Mahmoud, M.: Control of linear discrete-time systems by quantised feedback. IET Control Theory Appl. 6, 2095–2102 (2012)

    Article  MathSciNet  Google Scholar 

  6. Wu, L., Zheng, W.: Passivity-based sliding mode control of uncertain singular time-delay systems. Automatica 45, 2120–2127 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zheng, B., Yang, G.: Decentralized sliding mode quantized feedback control for a class of uncertain large-scale systems with dead-zone input nonlinearity. Nonlinear Dyn. 71, 417–427 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zheng, B., Yang, G.: \(H_2\) control of linear uncertain systems considering input quantization with encoder/decoder mismatch. ISA Trans. 52, 577–582 (2013)

    Article  MathSciNet  Google Scholar 

  9. Zheng, B., Xue, Y.: A sliding sector approach to quantized feedback variable structure control. Int. J. Control Automation Syst. 11, 1177–1186 (2013)

    Article  Google Scholar 

  10. Jiang, Z., Liu, T.: Quantized nonlinear control-a survey. Acta Automatica Sinica 39, 1820–1830 (2013)

    MathSciNet  Google Scholar 

  11. Mera, M., Castaños, F., Poznyak, A.: Quantised and sampled output feedback for nonlinear systems. Int. J. Control 87, 2475–2487 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fu, M., Xie, L.: The sector bound approach to quantized feedback control. IEEE Trans. Automatic Control 50, 1698–1711 (2005)

    Article  MathSciNet  Google Scholar 

  13. Gao, H., Chen, T.: A new approach to quantised feedback control systems. Automatica 44, 534–542 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gao, H., Chen, T.: \(H_\infty \) estimation for uncertain systems with limited communication capacity. IEEE Trans. Automatic Control 52, 2070–2084 (2007)

    Article  MathSciNet  Google Scholar 

  15. Xia, Y., Yan, J., Shi, P., Fu, M.: Stability analysis of discrete-time systems with quantized feedback and measurements. IEEE Trans. Ind. Inform. 9, 313–324 (2013)

    Article  Google Scholar 

  16. Liu, M., You, J.: Observer-based controller design for networked control systems with sensor quantisation and random communication delay. Int. J. Syst. Sci. 43, 1901–1912 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lee, T., Park, J., Lee, S., Kwon, O.: Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int. J. Control 86, 107–119 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lee, T., Park, J., Kwon, O., Lee, S.: Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw. 46, 99–108 (2013)

    Article  MATH  Google Scholar 

  19. Ge, Y., Wang, J., Li, C., Zhang, L.: Robust \(H_\infty \) output feedback control with partly quantised information. IET Control Theory Appl. 7, 523–536 (2013)

    Article  MathSciNet  Google Scholar 

  20. Zhou, B., Duan, G., Lam, J.: On the absolute stability approach to quantized feedback control. Automatica 46, 337–346 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang, J., Lam, J., Xia, Y.: Observer-based output feedback control for discrete systems with quantised inputs. IET Control Theory Appl. 5, 478–485 (2011)

    Article  MathSciNet  Google Scholar 

  22. Zhou, S., Wang, L., Zheng, W.: \(H_\infty \) filter design for nonlinear parameter-varying systems with quantized measurements. J. Frankl. Inst. 349, 1781–1807 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yang, W., Liu, M., Shi, P.: \(H_\infty \) filtering for nonlinear stochastic systems with sensor saturation, quantization and random packet losses. Signal Process. 92, 1387–1396 (2012)

    Article  Google Scholar 

  24. Lu, R., Zhou, X., Wu, F., Xue, A.: Quantized \(H_\infty \) output feedback control for linear discrete-time systems. J. Frankl. Inst. 350, 2096–2108 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser, Boston (2001)

    Book  MATH  Google Scholar 

  26. Tarbouriech, S., Gouaisbaut, F.: Control design for quantized linear systems with saturations. IEEE Trans. Automatic Control 57, 1883–1889 (2012)

    Article  MathSciNet  Google Scholar 

  27. Su, H., Chen, M., Lam, J., Lin, Z.: Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback. IEEE Trans. Circ. Syst.-I: Regul. Pap. 60, 1881–1889 (2013)

  28. Su, H., Chen, M., Wang, X., Lam, J.: Semiglobal observer-based leader-following consensus with input saturation. IEEE Trans. Ind. Electron. 61, 2842–2850 (2014)

  29. Abbaszadeh, M., Marquez, H.J.: LMI optimization approach to robust \(H_\infty \) observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems. Int. J. Robust Nonlinear Control 19, 313–340 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Sayyaddelshad, S., Gustafsson, T.: \(H_\infty \) observer design for uncertain nonlinear discrete-time systems with time-delay: LMI optimization approach. Int. J. Robust Nonlinear Control 25, 1514–1527 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu, S.: Robust \(H_\infty \) filtering for a class of discrete-time uncertain nonlinear systems with state delay. IEEE Trans. Circ. Syst.-I: Fundam. Theory Appl. 49, 1853–1859 (2002)

    Article  Google Scholar 

  32. Xu, S., Chen, T.: Robust \(H_\infty \) control for uncertain stochastic systems with state delay. IEEE Trans. Automatic Control 47, 2089–2094 (2002)

    Article  Google Scholar 

  33. Chen, K., Fong, I.K.: Stability analysis and output-feedback stabilisation of discrete-time systems with an interval time-varying state delay. IET Control Theory Appl. 4, 563–572 (2010)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the following grants: The Startup Foundation for Introducing Talent of NUIST (No. S8113107001), Natural Science Fundamental Research Project of Jiangsu Colleges and Universities (No. 15KJB120007), National Natural Science Foundation of P.R. China (No. 61503190), Outstanding Youth Science Fund Award of Jiangsu Province (No. BK20140045) and Jiangsu Agriculture Science and Technology Innovation Fund (No. CX(12)3050).

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Authors and Affiliations

  1. B-DAT, CICAEET, School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, People’s Republic of China

    Gongfei Song, Tao Li & Yuanlu Li

  2. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210042, Jiangsu, People’s Republic of China

    Junwei Lu

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  1. Gongfei Song
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  2. Tao Li
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  3. Yuanlu Li
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  4. Junwei Lu
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Correspondence to Gongfei Song.

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Song, G., Li, T., Li, Y. et al. Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator. Nonlinear Dyn 83, 305–317 (2016). https://doi.org/10.1007/s11071-015-2327-3

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  • DOI: https://doi.org/10.1007/s11071-015-2327-3

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