Skip to main content
SpringerLink
Log in

A New Integral Inequality Approach for Extended Dissipative Filters Design of Singular Markovian Jump Systems with Discrete and Distributed Delays

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper studies the problem of reduced-order extended dissipative filters design for continuous-time singular Markovian jump systems with discrete and distributed delays. By proposing a new integral inequality, a sufficient condition based on linear matrix inequalities (LMIs) is presented to ensure the existence of the extended dissipative filters. Compared with the previous ones, the proposed method can sufficiently exploit the information on discrete and distributed delays. A set of slack matrices instead of fixed ones are introduced in the LMIs to find all solutions of the reduced-order filters, which can enhance the flexibility of the obtained result. Two numerical examples are provided to illustrate the effectiveness and advantages of the proposed filters design condition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. F. Cecilia, M. Jonathan, L. Pedro, C. Oliveira, An LMI approach for \(H_{2}\) and \(H_{\infty }\) reduced-order filtering of uncertain discrete-time Markov and Bernoulli jump linear systems. Automatica 95, 463–471 (2018)

    MathSciNet  MATH  Google Scholar 

  2. L. Dai, Singular Control Systems (Springer, Berlin, 1989)

    MATH  Google Scholar 

  3. M. Fang, L. Wang, Z. Wu, Asynchronous stabilization of Boolean Control Networks with stochastic switched signals. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2913088

    Article  Google Scholar 

  4. T. Feng, B. Wu, L. Liu, Y. Wang, Finite-time stability and stabilization of fractional-order switched singular continuous-time systems. Circuits Syst. Signal Process. (2019). https://doi.org/10.1007/s00034-019-01159-1

    Article  Google Scholar 

  5. Z. Feng, J. Lam, Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Trans. Neural Netw. 22, 976–981 (2012)

    Google Scholar 

  6. K. Han, J. Feng, X. Chang, Reduced-order partially mode-dependent energy-to-peak filter design for discrete-time Markov jump systems subject to quantizer faults and state-dependent noises. Circuits Syst. Signal Process. 34, 77–103 (2015)

    MathSciNet  Google Scholar 

  7. H. Huang, T. Huang, X. Chen, Reduced-order state estimation of delayed recurrent neural networks. Neural Netw. 98, 59–64 (2018)

    Google Scholar 

  8. H. Huang, T. Huang, Y. Cao, Reduced-order filtering of delayed static Neural Networks with Markovian jumping parameters. IEEE Trans. Neural Netw. 29(11), 5606–5618 (2018)

    MathSciNet  Google Scholar 

  9. X. Jiang, G. Xia, Z. Feng, Resilient \(H_{\infty } \) filtering for stochastic systems with randomly occurring gain variations, nonlinearities and channel fadings. Circuits Syst. Signal Process. (2019). https://doi.org/10.1007/s00034-019-01087-0

    Article  Google Scholar 

  10. S. Kim, Asynchronous dissipative filter design of nonhomogeneous Markovian jump fuzzy systems via relaxation of triple-parameterized matrix inequalities. Inf. Sci. 478, 564–579 (2019)

    MathSciNet  Google Scholar 

  11. X. Lin, X. Zhang, Y. Wang, Robust passive filtering for neutral-type neural networks with time-varying discrete and unbounded distributed delays. J. Frankl. Inst. 350, 966–989 (2013)

    MathSciNet  MATH  Google Scholar 

  12. G. Liu, J. Park, S. Xu, G. Zhuang, Robust non-fragile \(H_{\infty }\) fault detection filter design for delayed singular Markovian jump systems with linear fractional parametric uncertainties. Nonlinear Anal. Hybrid Syst. 32, 65–78 (2019)

    MathSciNet  MATH  Google Scholar 

  13. G. Liu, Z. Qi, S. Xu, Z. Li, Z. Zhang, \(\alpha \)-Dissipativity filtering for singular Markovian jump systems with distributed delays. Signal Process. 134, 149–157 (2017)

    Google Scholar 

  14. G. Liu, S. Xu, J. Park, G. Zhuang, Reliable exponential \(H_{\infty }\) filtering for singular Markovian jump systems with time-varying delays and sensor failures. Int. J. Robust Nonlinear Control 28, 4230–4245 (2018)

    MathSciNet  MATH  Google Scholar 

  15. M. Liu, Q. Wang, S. Qu, State estimation for discrete-time singular jump systems with non-accessible mode information. Circuits Syst. Signal Process. 31, 761–777 (2012)

    MathSciNet  MATH  Google Scholar 

  16. Y. Ma, M. Chen, Non-fragile \(H_{\infty }\) state feedback control for singular Markovian jump fuzzy systems with interval time-delay. Int. J. Mach. Learn. Cybern. 8, 1223–1233 (2017)

    Google Scholar 

  17. S. Rathinasamy, S. Murugesan, F. Alzahrani, Y. Ren, Quantized finite-time non-fragile filtering for singular markovian jump systems with intermittent measurements. Circuits Syst. Signal Process. (2019). https://doi.org/10.1007/s00034-019-01046-9

    Article  Google Scholar 

  18. J. Ren, Q. Zhang, Robust normalization and guaranteed cost control for a class of uncertain descriptor systems. Automatica 48(8), 1693–7169 (2012)

    MathSciNet  MATH  Google Scholar 

  19. J. Ren, Q. Zhang, Simultaneous robust normalization and delay-dependent robust \(H_{\infty }\) stabilization for singular time-delay systems with uncertainties in the derivative matrices. Int. J. Robust Nonlinear Control 25, 3528–3545 (2015)

    MathSciNet  MATH  Google Scholar 

  20. L. Rong, X. Peng, B. Zhang, A reduced-order fault detection filter design for polytopic uncertain continuous-time Markovian jump systems with time-varying delays. Int. J. Control Autom. Syst. 16, 1–15 (2018)

    MATH  Google Scholar 

  21. M. Sathishkumar, R. Sakthivel, C. Wang, B. Kaviarasan, S. Anthoni, Non-fragile filtering for singular Markovian jump systems with missing measurements. Signal Process. 142, 125–136 (2018)

    Google Scholar 

  22. H. Shen, Extended dissipative filtering for persistent dwell-time switched systems with packet dropouts. IEEE Trans. Syst. Man Cybern. 1–11 (2018). https://doi.org/10.1109/TSMC.2018.2866632

  23. H. Shen, S. Huo, J. Cao, T. Huang, Generalized state estimation for Markovian coupled networks under round-robin protocol and redundant channels. IEEE Trans. Cybern. 49(4), 1292–1301 (2019)

    Google Scholar 

  24. H. Shen, F. Li, Z. Wu, J. Park, V. Sreeram, Fuzzy-model-based nonfragile control for nonlinear singularly perturbed systems with semi-Markov jump parameters. IEEE Trans. Fuzzy Syst. 26(6), 3428–3439 (2018)

    Google Scholar 

  25. H. Shen, F. Li, S. Xu, V. Sreeram, Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE Trans. Autom. Control 63(8), 2709–2714 (2018)

    MathSciNet  MATH  Google Scholar 

  26. H. Shen, T. Wang, J. Cao, G. Lu, Y. Song, T. Huang, Nonfragile dissipative synchronization for Markovian memristive Neural Networks: a gain-scheduled control scheme. IEEE Trans. Neural Netw. 30(6), 1841–1853 (2018)

    MathSciNet  Google Scholar 

  27. Y. Shen, Z. Wu, P. Shi, G. Wen, Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes. Automatica 106, 8–17 (2019)

    MathSciNet  MATH  Google Scholar 

  28. P. Shi, Y. Zhang, M. Chadli, R.K. Agarwal, Mixed \(H_{\infty }\) and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Trans. Neural Netw. 27, 903–909 (2016)

    Google Scholar 

  29. Q. Sun, R. Fan, Y. Li, B. Huang, D. Ma, A distributed double-consensus algorithm for residential we-energy. IEEE Trans. Ind. Inform. 15(8), 4830–4842 (2019)

    Google Scholar 

  30. Q. Sun, R. Han, H. Zhang, J. Zhou, J. Guerrero, A multiagent-based consensus algorithm for distributed coordinated Control of distributed generators in the energy internet. IEEE Trans. Smart Grid. 6(6), 3006–3019 (2015)

    Google Scholar 

  31. Q. Sun, B. Huang, D. Li, D. Ma, Y. Zhang, Optimal placement of energy storage devices in microgrids via structure preserving energy function. IEEE Trans. Ind. Inform. 12(3), 1166–1179 (2016)

    Google Scholar 

  32. Q. Sun, Y. Zhang, H. He, D. Ma, H. Zhang, A novel energy function-based stability evaluation and nonlinear control approach for energy internet. IEEE Trans. Smart Grid. 8(3), 1195–1210 (2017)

    Google Scholar 

  33. Q. Sun, J. Zhou, J. Guerrero, H. Zhang, Hybrid three-phase or single-phase microgrid architecture with power management capabilities. IEEE Trans. Power Electron. 30(10), 5964–5977 (2015)

    Google Scholar 

  34. J. Tao, R. Lu, H. Su, Z. Wu, Asynchronous filtering of nonlinear Markov jump systems with randomly occurred quantization via T-S fuzzy models. IEEE Trans. Fuzzy Syst. 26, 1866–1877 (2019)

    Google Scholar 

  35. J. Wang, S. Ma, C. Zhang, M. Fu, \({H_\infty }\) state estimation via asynchronous filtering for descriptor Markov jump systems with packet losses. Signal Process. 154, 159–167 (2019)

    Google Scholar 

  36. Y. Wang, P. Shi, Q. Wang, D. Duan, Exponential \(H_{\infty }\) filtering for singular markovian jump systems with mixed mode-dependent time-varying delay. IEEE Trans. Circuits Syst. I Reg. Pap. 60, 2440–2452 (2013)

    MathSciNet  Google Scholar 

  37. Y. Wang, T. Zhang, J. Ren, J. Li, Network-based integral sliding mode control for descriptor systems with event-triggered sampling scheme. Int. J. Robust Nonlinear Control 29(10), 2757–2776 (2019)

    MathSciNet  MATH  Google Scholar 

  38. Z. Wu, S. Dong, P. Shi, D. Zhang, T. Huang, Reliable filter design of Takagi-Sugeno fuzzy switched systems with imprecise modes. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2018.2885505

    Article  Google Scholar 

  39. Z. Wu, S. Dong, H. Su, C. Li, Asynchronous dissipative control for Fuzzy Markov jump systems. IEEE Trans. Cybern. 48(8), 2426–2436 (2018)

    Google Scholar 

  40. Z. Wu, P. Shi, H. Su, J. Chu, Asynchronous \(L_2-L_{\infty }\) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica 50, 180–186 (2014)

    MathSciNet  MATH  Google Scholar 

  41. Z. Wu, H. Su, J. Chu, Delay-dependent \(H_{\infty }\) filtering for singular Markovian jump time-delay systems. Signal Process. 90, 1815–1824 (2010)

    MATH  Google Scholar 

  42. Z. Wu, H. Su, J. Chu, Robust stabilization for uncertain discrete singular systems with state delay. Int. J. Robust Nonlinear Control 18(16), 1532–1550 (2010)

    MathSciNet  MATH  Google Scholar 

  43. Z. Wu, H. Su, J. Chu, \(H_{\infty }\) filtering for singular Markovian jump systems with time delay. Int. J. Robust Nonlinear Control 20, 939–957 (2010)

    MathSciNet  MATH  Google Scholar 

  44. W. Xia, Q. Ma, J. Lu, G. Zhuang, Reliable filtering with extended dissipativity for uncertain systems with discrete and distributed delays. Int. J. Syst. Sci. 48, 2644–2657 (2017)

    MathSciNet  MATH  Google Scholar 

  45. Y. Xia, L. Li, M. Mahmoud, H. Yang, \(H_{\infty }\) filtering for nonlinear singular Markovian jumping systems with interval time-varying delays. Int. J. Syst. Sci. 43, 272–284 (2012)

    MathSciNet  MATH  Google Scholar 

  46. G. Yang, Y. Kao, B. Jiang, J. Yin, Delay-dependent \(H_{\infty }\) filtering for singular Markovian jump systems with general uncomplete transition probabilities. Appl. Math. Comput. 294, 195–215 (2017)

    MathSciNet  MATH  Google Scholar 

  47. H. Yang, D. Ye, Distributed fixed-time consensus tracking control of uncertain nonlinear multi-agent systems: a prioritized strategy. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2925123

    Article  Google Scholar 

  48. D. Ye, M. Chen, H. Yang, Distributed adaptive event-triggered fault-tolerant consensus of multi-agent systems with general linear dynamics. IEEE Trans. Cybern. 49(3), 757–767 (2019)

    Google Scholar 

  49. D. Ye, T. Zhang, Summation detector for false data injection attack in cyber-physical systems. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2915124

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

  51. X. Zhang, Q. Han, A less conservative method for designing \(H_{\infty }\) filters for linear time-delay systems. Int. J. Robust Nonlinear Control 19, 1376–1396 (2010)

    MathSciNet  MATH  Google Scholar 

  52. G. Zhuang, S. Xu, B. Zhang, J. Xia, Y. Chu, Y. Zou, Unified filters design for singular Markovian jump systems with time-varying delays. J. Frankl. Inst. 353, 739–3768 (2016)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61973070, 61433004, and 61627809, the Liaoning Revitalization Talents Program under Grant XLYC1802010, and in part by SAPI Fundamental Research Funds under Grant 2018ZCX22.

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Yufeng Tian & Zhanshan Wang

Authors
  1. Yufeng Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhanshan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanshan Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tian, Y., Wang, Z. A New Integral Inequality Approach for Extended Dissipative Filters Design of Singular Markovian Jump Systems with Discrete and Distributed Delays. Circuits Syst Signal Process 39, 2900–2921 (2020). https://doi.org/10.1007/s00034-019-01305-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01305-9

Keywords

Search

Navigation