Skip to main content
SpringerLink
Log in

Predictor-Based Control of Systems with State-Multiplicative Noise

  • Chapter
  • First Online:
Advances in H∞ Control Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 481))

  • 490 Accesses

Abstract

Linear, continuous-time systems with state-multiplicative noise and time-delayed input are considered. The problems of \(H_{\infty }\) state-feedback and output-feedback control are solved for these systems when uncertainty in their deterministic parameters is encountered. Cascaded sub-predictors of the Luenberger-type are applied that considerably increase the size of the input time delay that can be solved for. Two examples are given. The first is a practical control engineering design and the second is an illustrative example that compares several solution methods for the stochastic state-feedback control.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
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. Dragan, V., Morozan, T.: Mixed input-output optimization for time-varying Ito systems with state dependent noise. Dyn. Contin., Discret. Impuls. Syst. 3, 317–333 (1997)

    Article  MathSciNet  Google Scholar 

  2. Gershon, E., Shaked, U., Yaesh, I.: \(H_\infty \) Control and Estimation of State-Multiplicative Linear Systems. Lecture Notes in Control and Information Sciences, LNCIS, vol. 318. Springer, Berlin (2005)

    Google Scholar 

  3. Boukas, E.K., Liu, Z.K.: Deterministic and Stochastic Time Delay Systems. Birkhauser, Basel (2002)

    Book  Google Scholar 

  4. Gershon, E., Shaked, U.: Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems. Lecture Notes in Control and Information Sciences, LNCIS, vol. 439. Springer, Berlin (2013)

    MATH  Google Scholar 

  5. Xu, S., Lam, J., Chen, T.: Robust \(H_\infty \) control for uncertain discrete stochastic time-delay systems. Syst. Control Lett. 51, 203–215 (2004)

    Article  MathSciNet  Google Scholar 

  6. Yue, D., Tian, E., Zhang, Y.: Stability analysis of discrete systems with stochastic delay and its applications. Int. J. Innov. Comput., Inf. Control 5(8), 2391–2403 (2009)

    Google Scholar 

  7. Kolmanovskii, V., Richard, J.P.: Stability of some linear systems with delays. IEEE Trans. Autom. Control 44, 984–989 (1999)

    Article  MathSciNet  Google Scholar 

  8. Huang, Y.P., Zhou, K.: Robust stability of uncertain time-delay systems. IEEE Trans. Autom. Control 45, 2169–2173 (2000)

    Article  MathSciNet  Google Scholar 

  9. Moon, Y.S., Park, P., Kwon, W.H., Lee, Y.S.: Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74, 1447–1455 (2001)

    Article  MathSciNet  Google Scholar 

  10. Niculescu, S.I.: Delay effects on stability: a robust control approach. Lecture Notes in Control and Information Sciences, vol. 269. Springer, London (2001)

    MATH  Google Scholar 

  11. Fridman, E.: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control Lett. 43, 309–319 (2001)

    Article  MathSciNet  Google Scholar 

  12. Kao, C.Y., Lincoln, B.: Simple stability criteria for systems with time-varying delays. Automatica 40, 1429–1434 (2004)

    Article  MathSciNet  Google Scholar 

  13. Fridman, E., Shaked, U.: Input-output approach to stability and \(L_2-\)gain analysis of systems with time-varying delays. Syst. Control Lett. 55, 1041–1053 (2006)

    Article  MathSciNet  Google Scholar 

  14. Gao, H., Chen, T.: New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control 52(2), 328–334 (2007)

    Article  MathSciNet  Google Scholar 

  15. Fridman, E., Orlov, Y.: Exponential stability of linear distributed parameter systems with time-varying delays. Automatica 45(2), 194–201 (2009)

    Article  MathSciNet  Google Scholar 

  16. Li, X., Gao, H., Yu, X.: A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delay. IEEE Trans. Syst., Man Cybernatics 41(5), 1275–1286 (2011)

    Article  Google Scholar 

  17. Li, X., Gao, H.: A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis. IEEE Trans. Autom. Control 56(9), 2172–2178 (2011)

    Article  MathSciNet  Google Scholar 

  18. Fridman, E.: Introduction to Time Delay Systems: Analysis and Control. Birkhauser, Basel (2014)

    Book  Google Scholar 

  19. Xu, S., Lam, J., Mao, X., Zou, Y.: A new LMI condition for delay-dependent robust stability of stochastic time-delay systems. Asian J. Control 7, 419–423 (2005)

    Article  MathSciNet  Google Scholar 

  20. Chen, W.H., Guan, Z., Lu, X.: Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Syst. Control Lett. 54, 547–555 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Li, H., Chen, B., Zhou, Q., Lin, C.: A delay-dependent approach to robust \(H_\infty \) control for uncertain stochastic systems with state and input delays. Circuits, Syst. Signal Process. 28, 169–183 (2009)

    Article  MathSciNet  Google Scholar 

  23. Smith, O.: A controller to overcome dead time. ISA 6(2), 28–33 (1959)

    Google Scholar 

  24. Manitius, A.Z., Olbrot, A.W.: Finite spectrum assignment problem for systems with delay. IEEE Trans. Autom. Control 24, 541–553 (1979)

    Article  MathSciNet  Google Scholar 

  25. Kwon, W., Pearson, A.: Feedback stabilization of linear systems with delayed control. IEEE Trans. Autom. Control 25(2), 266–269 (1980)

    Article  MathSciNet  Google Scholar 

  26. Artstein, Z.: Linear systems with delayed controls: a reduction. IEEE Trans. Autom. Control 27(4), 869–879 (1982)

    Article  MathSciNet  Google Scholar 

  27. Yue, D., Han, Q.L.: Delayed feedback control of uncertain systems with time-varying input delay. Automatica 41(2), 233–240 (2005)

    Article  MathSciNet  Google Scholar 

  28. Mazenc, F., Normand-Cyrot, D.: Reduction model approach for linear systems with sampled delayed inputs. IEEE Trans. Autom. Control 58(5), 1263–1268 (2013)

    Article  MathSciNet  Google Scholar 

  29. Klebaner, F.C.: Introduction to Stochastic Calculus with Applications. Imperial College Press, London (2012)

    Book  Google Scholar 

  30. Cvetkovski, Zdravko: Inequalities: Theorems, Techniques and Selected Problems. Springer, Berlin (2012)

    Book  Google Scholar 

  31. Shustin, E., Fridman, E.: On delay-derivative-dependent stability of systems with fast-varying delays. Automatica 43, 1649–1655 (2007)

    Article  MathSciNet  Google Scholar 

  32. Seborg, D.E., Edgar, T.F., Mellichamp, D.A.: Process Dynamics and Control, 2nd edn. Wiley and Sons, Hoboken (2004)

    Google Scholar 

  33. Vishnoi, V., Padhee, S., Kaur, G.: Controller performance evaluation for concentration control of isothermal continuous stirred tank reactor. Int. J. Sci. Res. Publ. 2(6), 1–7 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Holon Institute of Technology, Holon, Israel

    Eli Gershon

  2. School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

    Uri Shaked

Authors
  1. Eli Gershon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Uri Shaked
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eli Gershon .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Gershon, E., Shaked, U. (2019). Predictor-Based Control of Systems with State-Multiplicative Noise. In: Advances in H∞ Control Theory. Lecture Notes in Control and Information Sciences, vol 481. Springer, Cham. https://doi.org/10.1007/978-3-030-16008-1_12

Download citation

Publish with us

Policies and ethics

Search

Navigation