Quantized Control of Fuzzy Hidden MJSs

  • Shanling DongEmail author
  • Zheng-Guang Wu
  • Peng Shi
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 268)


The primary goal of this chapter is to investigate the GCC problem for nonlinear MJSs affected by quantization. Based on the HMM and the T–S fuzzy approach, we devote to designing an asynchronous controller, which can minimize the GCC performance index. Besides, the quantizer is also assumed to operate asynchronously with the plant, which is conditionally independent of the controller. The sector bound approach is used to handle quantization errors.


  1. 1.
    Zhu, S., Han, Q.-L., Zhang, C.: \(l_1\)-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: a linear programming approach. Automatica 50(8), 2098–2107 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gonzaga, C.A.C., Costa, O.L.V.: Stochastic stabilization and induced \(l_2\)-gain for discrete-time Markov jump Lur’e systems with control saturation. Automatica 50(9), 2397–2404 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    de Oliveira, A., Costa, O.: \({H}_2\)-filtering for discrete-time hidden Markov jump systems. Int. J. Control 90(3), 599–615 (2017)CrossRefGoogle Scholar
  4. 4.
    Graciani Rodrigues, C., Todorov, M.G., Fragoso, M.D.: \({H}_\infty \) control of continuous-time Markov jump linear systems with detector-based mode information. Int. J. Control 90(10), 2178–2196 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    do Valle Costa, O.L., Fragoso, M.D., Todorov, M.G.: A detector-based approach for the \({H}_ 2\) control of Markov jump linear systems with partial information. IEEE Trans. Autom. Control 60(5), 1219–1234 (2015)Google Scholar
  6. 6.
    Stadtmann, F., Costa, O.: \({H}_2\)-control of continuous-time hidden Markov jump linear systems. IEEE Trans. Autom. Control 62(8), 4031–4037 (2017)CrossRefGoogle Scholar
  7. 7.
    Wu, Z.-G., Shi, P., Shu, Z., Su, H., Lu, R.: Passivity-based asynchronous control for Markov jump systems. IEEE Trans. Autom. Control 62(4), 2020–2025 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Wu, Z.-G., Shi, P., Su, H., Lu, R.: Asynchronous \(l_2\)-\(l_\infty \) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica 50(5), 180–186 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zhang, L., Zhu, Y., Shi, P., Zhao, Y.: Resilient asynchronous \({H}_\infty \) filtering for Markov jump neural networks with unideal measurements and multiplicative noises. IEEE Trans. Cybern. 45(12), 2840–2852 (2015)CrossRefGoogle Scholar
  10. 10.
    Fu, M., Xie, L.: The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50(11), 1698–1711 (2005)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Tao, J., Lu, R., Su, H., Shi, P., Wu, Z.-G.: Asynchronous filtering of nonlinear Markov jump systems with randomly occurred quantization via T-S fuzzy models. IEEE Trans. Fuzzy Syst. 26(4), 1866–1877 (2018)Google Scholar
  12. 12.
    Wu, Z.-G., Dong, S., Su, H., Li, C.: Asynchronous dissipative control for fuzzy Markov jump systems. IEEE Trans. Cybern. 48(8), 2426–2436 (2018)CrossRefGoogle Scholar
  13. 13.
    Gao, H., Liu, X., Lam, J.: Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 39(2), 306–317 (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.National Laboratory of Industrial Control TechnologyInstitute of Cyber-Systems and Control, Zhejiang UniversityHangzhouChina
  2. 2.School of Electrical and Electronic EngineeringUniversity of AdelaideAdelaideAustralia
  3. 3.Victoria UniversityMelbourneAustralia

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