Skip to main content
SpringerLink
Log in

\(\mathscr {H}_\infty \) Filtering for Discrete-Time Nonlinear Systems

  • Chapter
  • First Online:
Dynamic Systems with Time Delays: Stability and Control

  • 913 Accesses

Abstract

This chapter is concerned with the \(\mathscr {H}_\infty \) problem for a class of nonlinear systems. It is supposed that the time delay belongs to a given interval, and the designed filter has additive gain variation satisfying Bernoulli distribution. A sufficient condition is established to guarantee asymptotically mean-square stable of the filtering error systems with a prescribed \(\mathscr {H}_\infty \) performance. Furthermore, an improved result of \(\mathscr {H}_\infty \) filtering for a linear system is also obtained. The filter parameters are obtained by solving a set of linear matrix inequalities. Two examples, which includes a longitudinal flight system, are given to show the effectiveness of the proposed method.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Geromel JC, de Oliveria MC (2001) \(\cal{H}_2\) and \(\cal{H}_\infty \) robust filtering for convex bounded uncertain systems. IEEE Trans Autom Control 46:100–107

    Google Scholar 

  2. Shi P, Bonkas EK, Agarwal RK (1999) Kalman filtering for continuous time uncertain systems with Markovian jumping parameters. IEEE Trans Autom Control 44:1592–1597

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang J, Xia Y, Shi P (2009) Parameter-dependent robust \(\cal{H}_\infty \) filtering for uncertain discrete-time systems. Automatica 45:560–565

    MathSciNet  MATH  Google Scholar 

  4. Li J, Zhang Y, Pan Y (2015) Mean-square exponential stability and stabilization of stochastic singular systems with multiple time-varying delays. Circuits Syst Signal Process 34:1187–1210

    Article  MATH  Google Scholar 

  5. Li J, Li L (2015) Mean-square exponential stability for stochastic discrete-time recurrent neural networks with mixed time delays. Neuroocmputing 151:790–797

    Article  Google Scholar 

  6. Kim JH, Ahn SJ, Ahn S (2005) Guaranteed cost and \(\cal{H}_\infty \) filtering for discrete-time polytopic uncertain systems with time-delay. J Frankl Inst 342:365–378

    MathSciNet  MATH  Google Scholar 

  7. Liu H, Sun F, He K, Sun Z (2001) Robust \(\cal{H}_\infty \) filtering for uncertain discrete-time state-delayed systems. IEEE Trans Signal Process 49:1696–1703

    MathSciNet  Google Scholar 

  8. He Y, Liu GP, Rees D, Mu W (2009) \(\cal{H}_\infty \) filtering for discrete-time systems with time-varying delay. Signal Process 89:275–282

    Google Scholar 

  9. You J, Gao H, Basin M (2013) Further improved results on \(\cal{H}_\infty \) filtering for discrete time-delay systems. Signal Process 93:1845–1852

    Google Scholar 

  10. Wang Z, Ho DWC, Liu Y, Liu X (2009) Robust \(\cal{H}_\infty \) control for a class of nonlinear discrete-time delay stochastic systems with missing measurements. Automatica 45:684–691

    MathSciNet  MATH  Google Scholar 

  11. Li H, Gao Y, Shi P, Lam H (2015) Observer-based fault detection for nonlinear system with sensor fault and limited communication capacity. IEEE Trans Autom Control 61:2745–2751

    Article  MathSciNet  MATH  Google Scholar 

  12. Xu S (2002) Robust \(\cal{H}_\infty \) filtering for a class of discrete-time uncertain nonlinear systems with state delay. IEEE Trans Circuits Syst I: Fundam Theory and Appl 49:1853–1859

    Google Scholar 

  13. Gao H, Lam J, Wang C (2005) Induced \(\cal{L}_2\) and generalized \(\cal{H}_2\) filtering for systems with repeated scalar nonlinearities. IEEE Trans Signal Process 53:4215–4226

    MathSciNet  MATH  Google Scholar 

  14. Yang R, Shi P, Liu G (2011) Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts. IEEE Trans Autom Control 56:2655–2660

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang J, Xia Y, Tao R (2009) New Results on \(\cal{H}_\infty \) filtering for fuzzy time-delay systems. IEEE Trans Fuzzy Syst 17:128–137

    Google Scholar 

  16. Huang S, He X, Zhang N (2011) New results on \(\cal{H}_\infty \) filter for nonlinear systems with time delay via T-S fuzzy model. IEEE Trans Fuzzy Syst 19:193–199

    Google Scholar 

  17. Su Y, Chen B, Lin C, Zhang H (2009) A new fuzzy \(\cal{H}_\infty \) filter design for nonlinear continuous-time dynamic systems with time-varying delays. Fuzzy Sets Syst 160:3539–3549

    MathSciNet  MATH  Google Scholar 

  18. Wu YQ, Su H, Lu R, Wu ZG, Shu Z (2015) Passivity-based non-fragile control for Markovian-jump systems with aperiodic sampling. Syst Control Lett 84:35–43

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang D, Cai WJ, Xie LH, Wang QG (2015) Non-fragile distributed filtering for T-S fuzzy systems in sensor networks. IEEE Trans Fuzzy Syst 23:1883–1980

    Article  Google Scholar 

  20. Zhang D, Shi P, Zhang WA (2016) Non-fragile distributed filtering for fuzzy systems with multiplicative gain variation. Signal Process 121:102–110

    Article  Google Scholar 

  21. Liu Y, Park JH, Guo B (2016) Non-fragile \(\cal{H}_\infty \) filtering for nonlinear discrete-time delay systems with randomly occurring gain variations. ISA Trans 63:196–203

    Google Scholar 

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

    MathSciNet  Google Scholar 

  23. Shen M, Park JH, Fei S (2018) Event-triggered non-fragile \(\cal{H}_\infty \) filtering of Markov jump systems with imperfect transmissions. Signal Process 149:204–213

    Google Scholar 

  24. Liu Y, Guo BZ, Park JH (2017) Non-fragile \(\cal{H}_\infty \) filtering for delayed Takagi-Sugeno fuzzy systems with randomly occurring gain variations. Fuzzy Sets Syst 316:99–116

    MathSciNet  MATH  Google Scholar 

  25. Shen H, Wu ZG, Park JH (2015) Reliable mixed passive and \(\cal{H}_\infty \) for semi-Markov jump systems with randomly occurring uncertainties and sensor failures. Int J Robust Nonlinear Control 25:3231–3235

    MathSciNet  MATH  Google Scholar 

  26. Seuet A, Gouaisbaut F, Fridman E (2015) Stability of discrete-time systems with time-varying delay via a novel summation inequality. IEEE Trans Autom Control 60:2740–2745

    Article  MathSciNet  MATH  Google Scholar 

  27. Park PG, Ko JW, Jeong C (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47:235–238

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Yeungnam University, Gyeongsan-si, Korea (Republic of)

    Ju H. Park

  2. Division of Electronic Engineering, Chonbuk National University, Jeonju, Korea (Republic of)

    Tae H. Lee

  3. Control and Computer Engineering, North China Electric Power University, Beijing, China

    Yajuan Liu

  4. School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou, China

    Jun Chen

Authors
  1. Ju H. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tae H. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yajuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ju H. Park .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Park, J., Lee, T.H., Liu, Y., Chen, J. (2019). \(\mathscr {H}_\infty \) Filtering for Discrete-Time Nonlinear Systems. In: Dynamic Systems with Time Delays: Stability and Control. Springer, Singapore. https://doi.org/10.1007/978-981-13-9254-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation