Skip to main content
SpringerLink
Log in

Satisfactory control of discrete-time linear periodic systems

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

Abstract

In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities (LMIs), and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.

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. Z. Guo. A survey of satisfying control and estimation[C]// Proceedings of the 14th IFAC Congress. Beijing: Press of Tsinghua University, 1999: 443–447.

    Google Scholar 

  2. Z. Wang, Z. Guo. Variance-constrained dynamic output feedback control with regional pole assignment[J]. Chinese Journal of Automation, 1997, 9(1): 11–17.

    Google Scholar 

  3. Y. Wang, X. Xia. Consistency of Circular pole and upper state-variance constraints for discrete-time control systems[J]. Journal of Nanchang Institute of Aeronautical Technology, 1999, 13(4): 13–16 (in Chinese).

    Google Scholar 

  4. Y. Wang, Z. Guo. Consistency of circular pole and state variance constraints in state-feedback control[J]. Acta Automatic Sinica, 2001, 27(2): 207–213 (in Chinese).

    MathSciNet  Google Scholar 

  5. R. A. Meyer, C. S. Burrus. A unified analysis of multi-rate and periodically time-varying digital filters[J]. IEEE Transactions on Automatic Control, 1975, 22(3): 162–168.

    MathSciNet  Google Scholar 

  6. K. Tan, C. Wang. Robust stabilization of linear time-varying periodic systems and H-infinity control[J]. Chinese journal of Automation, 1997, 9(1): 53–56.

    Google Scholar 

  7. L. Xie, C. E. De Souza, Y. Wang. Robust control of discrete time uncertain dynamical systems[J]. Automatica, 1993, 29(4): 1133–1137.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Colaneri. Output stabilization via pole placement of discrete-time linear periodic systems[J]. IEEE Transactions on Automatic Control, 1991, 36(6): 739–742.

    Article  MathSciNet  Google Scholar 

  9. P. T. Kabamba. Monodromy eigenvalue assignment in linear periodic systems[J]. IEEE Transactions on Automatic Control, 1986, 31(10): 950–952.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Boyd, L. El. Ghaoui, E. Feron, et al. Linear Matrix Inequalities in Systems and Control Theory[M]. Philadelphia: SIAM, 1994.

    Google Scholar 

  11. L. Huang. Linear Algebra in System and Control Theory[M]. Beijing: Science Press, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Shiqian Liu, Jihong Zhu & JinChun Hu

Authors
  1. Shiqian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jihong Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. JinChun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Aviation Cooperation Research Foundation of China (No. 10577012) and the Chinese Postdoctoral Foundation (No. 2005038311).

Shiqian LIU received his B.S. in Mechanical Engineering from Petroleum University, Xi’an, in 1996, and Ph.D. in Control Science and Engineering from Nanjing University of Science and Technology Nanjing, in 2003. Since then, he has been an assistant researcher in Aeronautic Institution of Measurement and Control in Shanghai, 2004. His research interests are in intelligent flight control, fault diagnosis and embed systems. Dr. Liu is currently a postdoctoral researcher in Tsinghua University Beijing, China.

Ji-hong ZHU received his Ph.D. in Control Science and Engineering from Nanjing University of Science and Technology Nanjing, in 1995. Since then, he has been a postdoctoral researcher in Nanjing University of Aeronautics and Astronautics in 1997 and Tsinghua University in 1999 respectively, His research interests are in flight control, aerial Robot and intelligent control. Dr. Zhu is currently a professor in Department of Computer Science in Tsinghua University. Member IEEE, and serves on Chinese Artificial Intelligent Robot Board.

JinChun HU received his Ph.D. in Control Science and Engineering from Nanjing University of Science and Technology Nanjing, in 1998. Since then, he has been a postdoctoral researcher in Nanjing University of Aeronautics and Astronautics in 1999 and Tsinghua University in 2002 respectively, His research interests are in flight control, aerial Robot and intelligent control. Dr. Hu is currently assistant professor in department of computer science in Tsinghua University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, S., Zhu, J. & Hu, J. Satisfactory control of discrete-time linear periodic systems. J. Control Theory Appl. 5, 12–16 (2007). https://doi.org/10.1007/s11768-005-5077-9

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-005-5077-9

Keywords

Search

Navigation