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Resilient Dissipative Filtering for Uncertain Markov Jump Nonlinear Systems with Time-Varying Delays

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Abstract

The resilient dissipative filtering problem for a class of uncertain time-delay Markov jump nonlinear systems is studied in this paper. The nonlinear functions are assumed to belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system, and by constructing a new multiple Lyapunov–Krasovskii function, the sufficient conditions regarding the existence of desired resilient dissipative filters are obtained in terms of linear matrix inequalities, which ensure the filtering error system is stochastically stable and strictly dissipative. The designed filter can tolerate additive uncertainties in the filter gain matrix, which results from filter implementations. A numerical example is presented to show the effectiveness of the proposed theoretical results.

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References

  1. W.P. Blair, D.D. Sworder, Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria. Int. J. Control 21(5), 833–841 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  2. O. Costa, G. Benites, Robust mode-independent filtering for discrete-time Markov jump linear systems with multiplicative noises. Int. J. Control 86(5), 779–793 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. O. Costa, M. Fragoso, R. Marques, Discrete-Time Markov Jump Linear Systems (Springer, London, 2006)

    MATH  Google Scholar 

  4. H. Dong, Z. Wang, H. Gao, Distributed \(H_{\infty }\) filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks. IEEE Trans. Ind. Electron. 60(10), 4665–4672 (2013)

    Article  Google Scholar 

  5. E. Dynkin, Theory of Markov Processes (Dover, Mineola, 2006). (reprint of 1961 edition)

    MATH  Google Scholar 

  6. Z. Feng, J. Lam, Robust reliable dissipative filtering for discrete delay singular systems. Signal Process. 92(12), 3010–3025 (2012)

    Article  Google Scholar 

  7. A. Goncalves, A. Fioravanti, J. Geromel, \(H_{\infty }\) filtering of discrete time Markov jump linear systems through linear matrix inequalities. IEEE Trans. Autom. Control 54(6), 1347–1351 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. C.A.C. Gonzaga, O.L.V. Costa, Stochastic stabilization and induced \(l_{2}\)-gain for discrete-time Markov jump Lur’e systems with control saturation. Automatica 50(9), 2397–2404 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. C. Guan, Z. Fei, Z. Li et al., Improved \(H_{\infty }\) filter design for discrete-time Markovian jump systems with time-varying delay. J. Franklin Inst. 353(16), 4156–4175 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Hajiahmadi, B. De Schutter, H. Hellendoorn, Stabilization and robust \(H_{\infty }\) control for sector-bounded switched nonlinear systems. Automatica 50(10), 2726–2731 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. He, F. Liu, Exponential passive filtering for a class of nonlinear jump systems. J. Syst. Eng. Electron. 20, 829–837 (2009)

    Google Scholar 

  12. D.J. Hill, P.J. Moylan, Dissipative dynamic systems: basic input-output and state properties. J. Franklin Inst. 309, 327–357 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Hua, H. Tan, J. Chen et al., Robust delay-range-dependent non-fragile \(H_{\infty }\) filtering for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays. J. Franklin Inst. 352(3), 1318–1341 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. H.K. Khalil, Nonlinear Systems, 3rd edn. (Prentice Hall, New York, 2002)

    MATH  Google Scholar 

  15. J.H. Kim, Discrete passive filtering of singular systems with time-varying delay. Appl. Math. Sci. 6(81), 4047–4055 (2012)

    MathSciNet  MATH  Google Scholar 

  16. C. Li, H. An, Y. Feng, Dissipative filtering for linear discrete-time systems via LMI, in 2009 Chinese Control Decision Conference, Shanghai, China (2009), pp. 3866–3870

  17. A.I. Lur’e, Some Nonlinear Problem in the Theory of Automatic Control (H. M. Stationary Office, London, 1957)

    Google Scholar 

  18. M.S. Mahmoud, Resilient linear filtering of uncertain systems. Automatica 40(10), 1797–1802 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. K. Mathiyalagan, J.H. Park, R. Sakthivel et al., Robust mixed \(H_{\infty }\) and passive filtering for networked Markov jump systems with impulses. Signal Proces. 101, 162–173 (2014)

    Article  Google Scholar 

  20. R. Sakthivel, M. Sathishkumar, K. Mathiyalagan et al., Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties. Int. J. Adapt. Control Signal Process. (2016). doi:10.1002/acs.2680

    MATH  Google Scholar 

  21. H. Shen, L. Su, J.H. Park, Extended passive filtering for discrete-time singular Markov jump systems with time-varying delays. Signal Proces. 128, 68–77 (2016)

    Article  Google Scholar 

  22. G. Song, Y. Zhang, S. Xu, Stability and \(l_{2}\)-gain analysis for a class of discrete-time nonlinear Markovian jump systems with actuator saturation and incomplete knowledge of transition probabilities. IET Control Theory Appl. 6(17), 2716–2723 (2012)

    Article  MathSciNet  Google Scholar 

  23. W. Sun, H. Gao, O. Kaynak, Vibration isolation for active suspensions with performance constraints and actuator saturation. IEEE/ASME Trans. Mechatron. 20(2), 675–683 (2015)

    Article  Google Scholar 

  24. W. Sun, H. Gao, O. Kaynak, Finite frequency \(H_{\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2011)

    Article  Google Scholar 

  25. W. Sun, H. Gao, B. Yao, Adaptive robust vibration control of full-car active suspensions with electrohydraulic actuators. IEEE Trans. Control Syst. Technol. 21(6), 2417–2422 (2013)

    Article  Google Scholar 

  26. V. Ugrinovskii, H.R. Pota, Decentralized control of power systems via robust control of uncertain Markov jump parameter systems. Int. J. Control 78(9), 662–677 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Willems, Dissipative dynamical systems part I: general theory. Arch. Ration. Mech. Anal. 45(5), 321–351 (1972)

    Article  MATH  Google Scholar 

  28. Z. Wu, P. Shi, H. Su et al., Asynchronous \(l_{2}\)-\(l_{\infty }\) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica 50(1), 180–186 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  29. Z. Wu, P. Shi, H. Su, J. Chu, Dissipativity analysis for discrete-time stochastic neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 24(3), 345–355 (2013)

    Article  Google Scholar 

  30. S. Xu, T. Chen, J. Lam, Robust \(H_{\infty }\) filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Autom. Control 48(5), 900–907 (2003)

    Article  MATH  Google Scholar 

  31. H. Yan, H. Zhang, H. Shi et al., Robust \(H_{\infty }\) filtering for uncertain nonlinear stochastic systems with mode-dependent time-delays and Markovian jump parameters. Circuits Syst. Signal Process. 30(2), 303–321 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  32. X. Yang, W. Yang, J. Liu, Non-fragile strictly dissipative filter for discrete-time nonlinear systems with sector-bounded nonlinearities, in 2010 Chinese Control Decision Conference, Xuzhou, China (2010), pp. 4483–4488

  33. B. Zhang, W. Zheng, S. Xu, Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans Circuits Syst. I Regul. Pap. 60(5), 1250–1263 (2013)

    Article  MathSciNet  Google Scholar 

  34. L. Zhang, \(H_{\infty }\) estimation for discrete-time piecewise homogeneous Markov jump linear systems. Automatica 45(1), 2570–2576 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. L. Zhang, P. Shi, C. Wang et al., Robust \(H_{\infty }\) filtering for switched linear discrete-time systems with polytopic uncertainties. Int. J. Adapt. Control Signal Process. 20(6), 291–304 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. L. Zhang, Y. Zhu, P. Shi et al., Resilient asynchronous \( H_{\infty }\) filtering for Markov jump neural networks with unideal measurements and multiplicative noises. IEEE Trans. Cybern. 45(12), 2840–2852 (2015)

    Article  Google Scholar 

  37. L. Zhang, Y. Zhu, W. Zheng, Energy-to-peak state estimation for Markov jump RNNs with time-varying delays via nonsynchronous filter with nonstationary mode transitions. IEEE Trans. Neural Netw. Learn. Syst. 26(10), 2346–2356 (2015)

    Article  MathSciNet  Google Scholar 

  38. Y. Zhang, Y. Ou, Y. Zhou et al., Observer-based \(l_{2}\)-\( l_{\infty }\) control for discrete-time nonhomogeneous Markov jump Lur’e systems with sensor saturations. Neurocomputing 162, 141–149 (2015)

    Article  Google Scholar 

  39. Y. Zhu, L. Zhang, W. Zheng, Distributed H-infinity filtering for a class of discrete-time Markov jump Lur’e systems with redundant channels. IEEE Trans. Ind. Electron. 63(3), 1876–1885 (2016)

    Article  Google Scholar 

  40. G. Zhuang, Y. Wei, Non-Fragile \(H_{\infty }\) filter design for uncertain stochastic nonlinear time-delay Markovian jump systems. Circuits Syst. Signal Process. 33(11), 3389–3419 (2014)

    Article  MATH  Google Scholar 

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Acknowledgements

The work was supported in part by National High-Tech Research and Development Program of China (863 Program) (Grant No. 2015AA042303), National Natural Science Foundation of China (Grant No. U1613210), Shenzhen overseas innovation and entrepreneurship Research Program (KQCX2015033117354155), Shenzhen Fundamental Research Program (JCYJ2016428154842603).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Robotics and Intelligent System, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Yujie Zhang

  2. Key Laboratory of Human-Machine Intelligence-Synergy Systems, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Yongsheng Ou

  3. Shenzhen Institute of Information Technology, Shenzhen, 518172, China

    Yujie Zhang

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  1. Yujie Zhang
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  2. Yongsheng Ou
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Correspondence to Yongsheng Ou.

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Zhang, Y., Ou, Y. Resilient Dissipative Filtering for Uncertain Markov Jump Nonlinear Systems with Time-Varying Delays. Circuits Syst Signal Process 37, 636–657 (2018). https://doi.org/10.1007/s00034-017-0584-8

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  • DOI: https://doi.org/10.1007/s00034-017-0584-8

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