Skip to main content
SpringerLink
Log in

Non-Fragile H ∞ Guaranteed Cost Control for a Non-linear Stochastic System with Both Distributed Delays and Input Delays

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

Abstract

The problem of non-fragile H ∞ guaranteed cost control for a delay-dependent non-linear stochastic system is considered. Both distributed delays and input delays appear in the system. A delay-dependent stabilization condition is presented in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) technique. Furthermore, a sufficient condition of the existence of non-fragile H ∞ guaranteed cost controller is constructed. Finally, a numerical example is given to demonstrate the effectiveness and the feasibility of the proposed approaches in this paper.

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

Similar content being viewed by others

References

  1. M. Basin, E. Sanchez, R. Martinez-Zuniga, Optimal linear filtering for systems with multiple state and observation delays. Int. J. Innov. Comput. Inf. Control 3(5), 1309–1320 (2007)

    Google Scholar 

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

    Google Scholar 

  3. S. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory (SIAM, Philadelphia, 1994)

    Google Scholar 

  4. S. Chang, T. Peng, Adaptive guaranteed cost control of systems with uncertain parameters. IEEE Trans. Autom. Control 17, 474–483 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  5. W.H. Chen, Z.H. Guan, X.M. Lu, Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Syst. Control Lett. 54(6), 547–555 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. W.H. Chen, Z.H. Guan, X.M. Lu, Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays. J. Franklin Inst. 341(5), 419–430 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Dhawan, H. Kar, Optimal guaranteed cost control of 2-D discrete uncertain systems: an LMI approach. Signal Process. 87(12), 3075–3085 (2007)

    Article  MATH  Google Scholar 

  8. P. Dorato, Non-fragile controller design: an overview, in Proc. American Control Conference, Philadelphia (1998), pp. 2829–2831

    Google Scholar 

  9. K. Gu, An integral inequality in the stability problem of time-delay systems, in Proc. 39th IEEE Conference on Decision and Control, Sydney (2000), pp. 2805–2810

    Google Scholar 

  10. C.H. Lien, Delay-dependent and delay-independent guaranteed cost control for uncertain neutral systems with time-varying delays via LMI approach. Chaos Solitons Fractals 33(3), 1017–1027 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. C.H. Lien, Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input. Chaos Solitons Fractals 31(4), 889–899 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Z.Y. Lin, P. Shi, Robust guaranteed cost control for discrete-time systems with multiple delays in state. Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 11(1), 119–132 (2004)

    MathSciNet  MATH  Google Scholar 

  13. C.Y. Lu, W.J. Shyr, K.C. Yao, D.F. Chen, Delay-dependent approach to robust stability for uncertain discrete stochastic recurrent neural networks with interval time-varying delays. ICIC Express Lett. A 3(3), 457–464 (2009)

    Google Scholar 

  14. Y.C. Ma, Q.L. Zhang, Y.W. Ren, X.F. Zhang, H ∞ guaranteed cost control for time-delay uncertain discrete systems, in Proc. The 9th International Conference on Control, Automation, Robotics and Vision, Singapore (2006), pp. 1–6

    Chapter  Google Scholar 

  15. P.J. de Oliveira, R.C.L.F. Oliveira, V.J.S. Leite, V.F. Montagner, P.L.D. Peres, H ∞ guaranteed cost computation by means of parameter-dependent Lyapunov functions. Automatica 40(6), 1053–1061 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. J.Q. Qiu, H.J. Yang, P. Shi, Y.Q. Xia, Robust H ∞ control for class of discrete-time Markovian Jump systems with time-varying delays based on delta operator. Circuits Syst. Signal Process. 27(5), 627–643 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. J.Q. Qiu, H.J. Yang, J.H. Zhang, Z.F. Gao, New robust stability criteria for uncertain neural networks with interval time-varying delays. Chaos Solitons Fractals 39(2), 579–585 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Qiu, H. He, P. Shi, Delay-dependent guaranteed cost control for a non-linear stochastic system with distributed delays. Proc. Inst. Mech. Eng. Part I, J. Syst. Control Eng. 223, 763–772 (2009)

    Article  Google Scholar 

  19. P. Shi, H.J. Gao, A new delay-dependent stability criterion for stochastic systems with time delays. IET Control Theory App. 2(11), 966–973 (2008)

    Article  MathSciNet  Google Scholar 

  20. H.N. Wu, K.Y. Cai, H 2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty. Automatica 42(7), 1183–1188 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. S.Y. Xu, P. Shi, Y.M. Chu, Y. Zou, Robust stochastic stabilization and H ∞ control of uncertain neutral stochastic time-delay systems. J. Math. Anal. Appl. 314(1), 1–16 (2006)

    MathSciNet  MATH  Google Scholar 

  22. S.Y. Xu, J. Lam, G.H. Yang, J.L. Wang, Stabilization and H ∞ control for uncertain stochastic time-delay systems via non-fragile controllers. Asian J. Control 8(2), 197–200 (2006)

    Article  MathSciNet  Google Scholar 

  23. H.L. Xu, Y. Zou, S.Y. Xu, Non-fragile robust H ∞ control for uncertain 2-D delayed systems described by the general model. Int. J. Innov. Comput. Inf. Control A 5(10), 3179–3188 (2009)

    Google Scholar 

  24. L. Yu, An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure. Appl. Math. Comput. 162(3), 1325–1331 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. L. Yu, J. Chu, An LMI approach to guaranteed cost control of linear uncertain time-delay systems. Automatica 35(6), 1155–1159 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  26. D. Yue, J. Lam, Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delays. Optim. Control Appl. Methods 26(2), 85–105 (2005)

    Article  MathSciNet  Google Scholar 

  27. J.H. Zhang, P. Shi, J.Q. Qiu, Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems. J. Franklin Inst. 346, 676–690 (2009)

    Article  MathSciNet  Google Scholar 

  28. H.Y. Zhao, Q.W. Chen, S.Y. Xu, H ∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays. J. Franklin Inst. 346(10), 945–957 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. X.M. Zhu, C.C. Hua, S. Wang, State feedback controller design of networked control systems with time delay in the plant. Int. J. Innov. Comput. Inf. Control 4(2), 283–290 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, China

    Lianqing Su, Xiaodan Zhu & Jiqing Qiu

Authors
  1. Lianqing Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaodan Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiqing Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaodan Zhu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Su, L., Zhu, X. & Qiu, J. Non-Fragile H ∞ Guaranteed Cost Control for a Non-linear Stochastic System with Both Distributed Delays and Input Delays. Circuits Syst Signal Process 30, 1503–1520 (2011). https://doi.org/10.1007/s00034-011-9267-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-011-9267-z

Keywords

Search

Navigation