Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Dynamic Anti-Windup Control Design for Markovian Jump Delayed Systems with Input Saturation

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

Abstract

This paper deals with the problem of robust stabilization for Markovian jump delayed systems with partially known transition rates subject to input saturation. The problem we address is the design of dynamic anti-windup compensators, which guarantee that the resulting closed-loop constrained systems are robustly mean-square stable. By employing local sector conditions and an appropriate Lyapunov-Krasovskii function, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. E.K. Boukas, Free-weighting matrices delay-dependent stabilization for systems with time-varying delays. ICIC Express Lett. 2, 167–173 (2008)

    MathSciNet  Google Scholar 

  2. Y. Cao, Z. Lin, Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function. Automatica 39(7), 1235–1241 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Cao, Z. Lin, D.G. Ward, Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances. Automatica 40(7), 1221–1228 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Gao, Z. Fei, J. Lam, B. Du, Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays. IEEE Trans. Autom. Control 56(1), 223–229 (2011)

    Article  MathSciNet  Google Scholar 

  5. S. He, F. Liu, Controlling uncertain fuzzy neutral dynamic systems with Markov jumps. J. Syst. Eng. Electron. 21(3), 476–484 (2010)

    MathSciNet  Google Scholar 

  6. Y. He, M. Wu, J. She, Delay-dependent exponential stability of delayed neural networks with time-varying delay. IEEE Trans. Circuits Syst. II, Express Briefs 53(7), 553–557 (2006)

    Article  Google Scholar 

  7. C. Huang, C. Gung, Model based fuzzy control with affine T-S delayed models applied to nonlinear systems. Int. J. Innov. Comput. Inf. Control 8(5), 2979–2993 (2012)

    Google Scholar 

  8. Y. Kang, W. Shang, H. Xi, Estimating the delay-time for stability of Markovian jump bilinearsystems with saturating actuators. Acta Autom. Sin. 36(5), 762–767 (2010)

    Article  MathSciNet  Google Scholar 

  9. H.R. Karimi, Robust delay-dependent H ∞ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching parameters. IEEE Trans. Circuits Syst. I 58(8), 1910–1923 (2011)

    Article  MathSciNet  Google Scholar 

  10. H.R. Karimi, A sliding mode approach to H ∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. J. Franklin Inst. 349(4), 1480–1496 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. H.R. Karimi, H. Gao, New delay-dependent exponential H ∞ synchronization for uncertain neural networks with mixed time delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(1), 173–185 (2010)

    Article  Google Scholar 

  12. M.V. Kothare, M. Morari, Multiplier theory for stability analysis of anti-windup control systems, in Proceedings of 34th Conference on Decision and Control (1995) pp. 3767–3772

    Google Scholar 

  13. M.V. Kothare, P.J. Campo, M. Morari, C.N. Nett, A unified framework for the study of anti-windup designs. Automatica 30(12), 1869–1883 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Li, B. Chen, Q. Zhou, W. Qian, Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39(1), 94–102 (2009)

    Article  Google Scholar 

  15. H. Li, H. Gao, P. Shi, New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans. Neural Netw. 21(11), 1842–1847 (2010)

    Article  Google Scholar 

  16. P. Liu, Further results on the exponential stability criteria for time delay singular systems with delay-dependence. Int. J. Innov. Comput. Inf. Control 8(6), 4015–4024 (2012)

    Google Scholar 

  17. H. Liu, E.K. Boukas, Controller design of Markov jumping systems subject to actuator saturation. Automatica 42(3), 459–465 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Liu, L. Zhou, Static anti-windup synthesis for a class of linear systems subject to actuator amplitude and rate saturation. Acta Autom. Sin. 35(7), 1003–1006 (2009)

    Article  Google Scholar 

  19. E.F. Mulder, P.Y. Tiwari, M.V. Kothare, Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization. Automatica 45(3), 805–811 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. S.K. Nguang, W. Assawinchaichote, P. Shi, H ∞ filter for uncertain Markovian jump nonlinear systems: an LMI approach. Circuits Syst. Signal Process. 28, 853–874 (2007)

    Article  MathSciNet  Google Scholar 

  21. H. Shen, Y. Chu, S. Xu, Z. Zhang, Delay-dependent H ∞ Control for jumping delayed systems with two Markov processes. Int. J. Control. Autom. Syst. 9(3), 437–441 (2011)

    Article  Google Scholar 

  22. H. Shen, S. Xu, J. Zhou, J. Lu, Fuzzy H ∞ filtering for nonlinear Markovian jump neutral delayed systems. Int. J. Syst. Sci. 42(5), 767–780 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Shen, S. Xu, J. Lu, J. Zhou, Passivity based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays. J. Franklin Inst. 349(5), 1665–1680 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. H. Shen, S. Xu, X. Song, G. Shi, Passivity-based control for Markovian jump systems via retarded output feedback. Circuits Syst. Signal Process. 31(1), 189–202 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  25. P. Shi, M. Karan, C.Y. Kaya, Robust Kalman filter design for Markovian jump linear systems with norm-bounded unknown nonlinearities. Circuits Syst. Signal Process. 24(2), 135–150 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. P. Shi, M. Mahmoud, S.K. Nguang, A. Ismail, Robust filtering for jumping systems with mode-dependent delays. Signal Process. 86(1), 140–152 (2006)

    Article  MATH  Google Scholar 

  27. X. Song, S. Xu, Robust stabilization of state delayed T-S fuzzy systems with input saturation via dynamic anti-windup fuzzy design. Int. J. Innov. Comput. Inf. Control 7(12), 6665–6676 (2011)

    Google Scholar 

  28. R. Song, H. Zhang, Y. Luo, Q. Wei, Optimal control laws for time-delay systems with saturating actuators based on heuristic dynamic programming. Neurocomputing 73, 3020–3027 (2010)

    Article  Google Scholar 

  29. X. Su, P. Shi, L. Wu, Y. Song, A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay. IEEE Trans. Fuzzy Syst. (2012). doi:10.1109/TFUZZ.2012.2196522

    Google Scholar 

  30. Y. Tang, J. Fang, Q. Miao, Synchronization of stochastic delayed neural networks with Markovian switching and its application. Int. J. Neural Syst. 19(1), 43–56 (2009)

    Article  MathSciNet  Google Scholar 

  31. Y. Wang, L. Xie, C.E. Souza, Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19(2), 139–149 (1992)

    Article  Google Scholar 

  32. G. Wang, Q. Zhang, V. Sreeram, Partially mode-dependent H ∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities. Signal Process. 90(2), 548–556 (2010)

    Article  MATH  Google Scholar 

  33. L. Wu, W. Zheng, Fault detection filter design for Markovian jump singular systems with intermittent measurements. IEEE Trans. Signal Process. 59(7), 3099–3109 (2011)

    Article  MathSciNet  Google Scholar 

  34. L. Wu, P. Shi, H. Gao, C. Wang, H ∞ filtering for 2D Markovian jump systems. Automatica 44(7), 1849–1858 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  35. Z. Wu, H. Su, J. Chu, Delay-dependent H ∞ control for singular Markovian jump systems with time delay. Optim. Control Appl. Methods 30(5), 443–461 (2009)

    Article  MathSciNet  Google Scholar 

  36. Z. Wu, H. Su, J. Chu, Delay-dependent robust exponential stability of uncertain singular systems with time delays. Int. J. Innov. Comput. Inf. Control 6(5), 2275–2283 (2010)

    Google Scholar 

  37. L. Wu, X. Su, P. Shi, J. Qiu, Model approximation for discrete-time state-delay systems in the T-S fuzzy framework. IEEE Trans. Fuzzy Syst. 19(2), 366–378 (2011)

    Article  Google Scholar 

  38. L. Wu, X. Su, P. Shi, J. Qiu, A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 41(1), 273–286 (2011)

    Article  Google Scholar 

  39. L. Xie, Output feedback H ∞ control of systems with parameter uncertainty. Int. J. Control 63(4), 741–750 (1996)

    Article  MATH  Google Scholar 

  40. S. Xu, J. Lam, X. Mao, Delay-dependent H ∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. I 54(9), 2070–2077 (2007)

    Article  MathSciNet  Google Scholar 

  41. X. Yao, L. Wu, W. Zheng, C. Wang, Passivity analysis and passification of Markovian jump systems. Circuits Syst. Signal Process. 29(4), 709–725 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  42. S.S. Yoon, J.K. Park, T.W. Yoon, Dynamic anti-windup scheme for feedback linearizable nonlinear control systems with saturating inputs. Automatica 44(12), 3176–3180 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  43. L. Zaccarian, D. Nesic, A.R. Teel, \(\mathcal{L}_{2}\) anti-windup for linear dead-time systems. Syst. Control Lett. 54(12), 1205–1217 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  44. Y. Zhang, Y. He, M. Wu, J. Zhang, Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices. Automatica 47(1), 79–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  45. B. Zhang, W. Zheng, S. Xu, On robust H ∞ filtering of uncertain Markovian jump time-delay systems. Int. J. Adapt. Control Signal Process. 26(2), 138–157 (2012)

    Article  MathSciNet  Google Scholar 

  46. X. Zhao, Q. Zeng, New robust delay-dependent stability and H ∞ analysis for uncertain Markovian jump systems with time-varying delays. J. Franklin Inst. 347, 863–874 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant 61104007, the Key Foundation of Natural Science for Colleges and Universities in Anhui province under grant KJ2012A049, the Research Foundation for Young Scientists of Anhui University of Technology under Grant QZ201112.

Author information

Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Junjie Zhao

  2. School of Electrical Engineering and Information, Anhui University of Technology, Ma’anshan, 243002, China

    Jing Wang & Hao Shen

Authors
  1. Junjie Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hao Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hao Shen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, J., Wang, J. & Shen, H. Dynamic Anti-Windup Control Design for Markovian Jump Delayed Systems with Input Saturation. Circuits Syst Signal Process 32, 2213–2229 (2013). https://doi.org/10.1007/s00034-013-9560-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-013-9560-0

Keywords

Search

Navigation