Skip to main content
SpringerLink
Log in

H-infinity output feedback control for descriptor systems with delayed states

  • Regular Papers
  • Published:
Journal of Control Theory and Applications Aims and scope Submit manuscript

Abstract

This paper considers the H-infinity dynamic output feedback control for descriptor systems with delay in states. The controller is a descriptor system without delay. Several equivalent sufficient conditions for the existence of one descriptor dynamic controller without impulsive models are given. Furthermore the explicit expression of the desired controller is obtained. The detailed design of the controller is presented using the cone complementarity linearization iterative algorithm and the LMI method. A numerical example is shown to illustrate the designed method.

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. C. L. Byrnes, A. Isidori. Output regulation for nonlinear systems: an overview [C] // Proc. of 37th IEEE Conf. Decision and Control. Tampa, Florida, USA, 1998:3069–3074.

  2. V. Venkatasubramanian, H. Schattler, J. Zaborszky. Local bifurcations and feasibiling regions in differential-algebraic systems [J]. IEEE Trans. on Automatic Control, 1995,40(12): 1992–2013.

    Article  MATH  Google Scholar 

  3. D. G. Luenberger. Singular dynamic Leontief systems [J]. Econometrics, 1997,45(5):991–995.

    Google Scholar 

  4. S. S. Sastry, C. A. Desoer. Jump behavior of circuits and systems [J]. IEEE Trans, on Circuits and Systems, 1981,28(5): 1109–1124.

    Article  MATH  Google Scholar 

  5. J. D. Aplevich. Implicit Linear Systems [M], Berlin, Germany: Springer-Verlag, 1991.

    Google Scholar 

  6. S.L. Campbell. Singular System of Differential Equations II [M]. San Franciso, CA: Pitman, 1982.

    Google Scholar 

  7. L. Dai. Singular Control Systems [M]. New York: Springer-Verlag, 1989.

    Google Scholar 

  8. J. H. Lee, S. W. Kim, W. H. Kwon. Memoryless H∞ controllers for state delayed systems [J]. IEEE Trans. on Automatic Cortrol, 1994,39(1):159–162.

    Article  MATH  Google Scholar 

  9. S. L. Campbell. Singular linear systems of differential equtions with delays [J]. Applicable Analysis II, 1980,2(1):129–136.

    Article  Google Scholar 

  10. B. Lee, J. G. Lee. Robust stability and Stabilization of linear delayed systems with structured uncertainty [J]. Automatica, 1999,35(6):1149–1154.

    Article  MATH  Google Scholar 

  11. Xi Li, Carlos E. De Souza. Criteria for robust stabilization of uncertain linear systems with state delay [J]. Automatica, 1997,33(9):1657–1662.

    Article  Google Scholar 

  12. M. Jankovic. Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems [J]. IEEE Trans, on Automatic Control, 2001,46(7):1048–1060.

    Article  MATH  Google Scholar 

  13. H. Y. Su, J. Chu. Stabilization of a class of uncertain time-delay systems containing saturating actuators [J]. Int. J. of Systems Science, 1999, 30(10):1193–1203.

    MATH  Google Scholar 

  14. H. H. Choi, M.J. Chung. Robust observer-based Ho, controller design for linear uncertain time-delay systems [J]. Automatica, 1997,33(9):1749–1752.

    Article  Google Scholar 

  15. E. Fridman, U. Shaked. A descriptor system approach to Hoc control of linear time-delay systems [J]. IEEE Trans, on Automatic Control, 2002,47(2):253–270.

    Article  Google Scholar 

  16. J. E. Feng, Z. L. Cheng, S. P. Ma. Singular linear-quadratic optimal control problem for a class of discrete singular systems with multiple time-delays [J]. Int. J. of Systems and Sciences, 2003,34(4): 293–301.

    Article  MATH  Google Scholar 

  17. S. Xu, J. Lam, L. Zhang. Robust D-stability analysis for uncertain discrete singular systems with state delay [J]. IEEE Trans, on Circuits and Systems I, 2002,49(4):551–555.

    Article  Google Scholar 

  18. U. Ascher, L. R. Petzold. the numercial solution of delay differential algebraic equtions of retarded and neutral type [J]. SIAM J. Numerical Analysis, 1995,32(5):1635–1657.

    Article  MATH  Google Scholar 

  19. W. Zhu, L. Petzold. Ayamptotic stability of linear delay differential algebraic equations and numerical methods [J]. Applied Numerical Mathematics, 1997,24(2):247–264.

    Article  MATH  Google Scholar 

  20. Pierdomenico Pepe, Erik I. Verriest On the stability of coupled delay differential and continuous time difference equations [J]. IEEE Trans. on Automatic Control, 2003,48(8):1422–1427.

    Article  Google Scholar 

  21. S. Xu, P. V. Dooren, R. Stefan, et al. Robust stability and stabilization for singular systems with state delay and parameter uncertainty [J] IEEE Trans, on Automatic Control, 2002,47(7): 1122–1128.

    Article  Google Scholar 

  22. J. Feng, S. Zhu, Z Cheng. Guaranteed cost control of linear uncertain singular time-delay systems [C] // Proc. 41 th IEEE Conf. Decision and Control. Las Vegas, Nevada USA,2002:1802–1807.

  23. J. Feng, Z Cheng. Roubust H∞ control of uncertain singular systems with delay in state [J]. Control Theory & Applications, 2004,21(4):158–164.

    MATH  Google Scholar 

  24. X. Guan, Q. Zhang. H∞ State feedback control of singular delay systems [J]. Automatization and Instrument, 2002,18(5):1–3.

    Google Scholar 

  25. S. S. Hung, T. T. Lee. Memoryless H∞ controller for singular systems with delayed state and control [J]. J. of Frankin Institute, 1999,33(6):911–923.

    Article  Google Scholar 

  26. Y. Liu, X. Xie. Theory and Applicationg of Large-scale Dynamic Systems (Vol. 8) Stability, Stabization and Control for Delay Singular Systems [M]. Guangzhou: The South China University of Technology Press, 1998.

    Google Scholar 

  27. L. El Ghaoui, F. Oustry, M. AitRami. A cone complementarity linearization algorithm for static output-feedback and related problems [J]. IEEE Trans, on Automatic Control, 1997,42(8):1171–1176.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and System Sciences, Shandong University, 250100, Jinan, Shandong, China

    Jun’e Feng & Zhaolin Cheng

  2. School of Control Science and Engineering, Shandong University, 250061, Jinan, Shandong, China

    Peng Cui

Authors
  1. Jun’e Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhaolin Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by Mathematics Tianyuan Foundation of China (No. 10426021).

Jun’e FENG was born in Shandong Province, China, in 1971. She received the M.S. degree and the Ph. D. degree from Shandong University, in 1997 and 2003, respectively. She is now a teacher of School of Mathematics and System Sciences at Shandong University. Her research interests are in linear and nonlinear I stochastic systems, singular systems. E-mail: fengjune@sdu.edu.cn.

Peng CUI was born in Shandong Province, China, in 1972. He received the M.S. degree from Shandong University in 1999. He is now a Ph. D. candidate of School of Control Science and Engineering at Shandong University. His research interests are in linear systems and singular systems.

Zhaolin CHENG was born in Ninbo, China, in December 1939. He graduated from the Mathematics Department of Fudan University, Shanghai, China, in 1963. Since then, he has been a member of the faculty of the Mathematics Department of Shandong University Jinan, China, Where he is currently a professor. His current research interests are in linear system theory including singular systems, robust control, and macro-economic control systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, J., Cui, P. & Cheng, Z. H-infinity output feedback control for descriptor systems with delayed states. J. Control Theory Appl. 3, 342–347 (2005). https://doi.org/10.1007/s11768-005-0022-5

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-005-0022-5

Keywords

Search

Navigation