Skip to main content
SpringerLink
Log in

Enhanced LMI representations for H2 performance of polytopic uncertain systems: Continuous-time case

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

Based on two recent results, several new criteria of H2 performance for continuous-time linear systems are established by introducing two slack matrices. When used in robust analysis of systems with polytopic uncertainties, they can reduce conservatism inherent in the earlier quadratic method and the established parameter-dependent Lyapunov function approach. Two numerical examples are included to illustrate the feasibility and advantage of the proposed representations.

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. C. de Oliveira, J. Bernussou, J. C. Geromel. A New Discrete-time Robust Stability Condition. Systems & Control Letters, vol. 37, no. 4, pp. 261–265, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Apkarian, H. D. Tuan, J. Bernussou. Analysis, Eigenstructure Assignment and H2 Multi-channel Synthesis with Enhanced LMI Characterizations. In Proceedings of the 39th IEEE Conference on Decision and Control, Australia, pp. 1489–1494, 2000.

  3. P. Apkarian, H. D. Tuan, J. Bernussou. Continuous-time Analysis, Eigenstructure Assignment, and H2 Synthesis with Enhanced Linear Matrix Inequalities (LMI) Characterizations. IEEE Transactions on Automatic Control, vol. 46 no. 12, pp. 1941–1946, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  4. U. Shaked. Improved LMI Representations for Analysis and the Design of Continuous-Time Systems with Polytopic Type Uncertainty. IEEE Transactions on Automatic Control, vol. 46, no. 4, pp. 652–656, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. D. Tuan, P. Apkarian, T. Q. Nguyen. Robust and Reduced-order Filtering: New LMI-based Characterizations and Methods. IEEE Transactions on Signal Processing, vol. 49, no. 12, pp. 2975–2984, 2001.

    Article  Google Scholar 

  6. H. J. Gao, C. H. Wang. Robust Energy-to-peak Filtering with Improved LMI Representations. IEE Proceedings-Vision, Image and Signal Processing, vol. 150, no. 2, pp. 82–89, 2003.

    Article  Google Scholar 

  7. H. J. Gao, C. H. Wang. New Approaches to Robust and Filtering for Uncertain Discrete-time Systems. Science In China (Series F), vol. 46, no. 5, pp. 356–370, 2003.

    MathSciNet  Google Scholar 

  8. J. Daafouz, J. Bernussou. Poly-quadratic Stability and Hinf Performance for Discrete Systems with Time Varying Uncertainties. In Proceedings of the 40th IEEE Conference on Decision and Control, Oriando, Florida USA, pp. 267–272, 2001.

  9. L. H. Xie, L. L. Hu, D. Zhang, H. S. Zhang. Robust Filtering for Uncertain Discrete-Time: An Improved LMI Approach. In Proceedings of the 42nd IEEE Conference on Decision and Control, Hawaii, USA, pp. 906–911, 2003.

  10. P. J. de Oliveira, R. C. L. F. Oliveria, V. J. S. Leite, V. F. Montagner, P. L. D. Peres. Hinf Guaranteed Cost Computation by Means of Parameter-dependent Lyapunov Functions. Automatica, vol. 40, no. 6, pp. 1053–1061, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  11. T. Li, Y. M. Jia. Improved LMI Representations for Bounded Real Criterion of Systems with Polytopic Type Uncertainty. In Proceedings of the IEEE American Control Conference, Denver, Colorado, pp. 851–856, June 4–6, 2003.

  12. J. Doyle, K. Glover, P. Khargonchar, B. Francis. State-space Solutions to Standard H2 and Hinf Control Problems. IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831–847, 1989.

    Article  MATH  Google Scholar 

  13. C. W. R. Domingos, P. D. Peres. An LMI Condition for The Robust Stability of Uncertain Continuous-time Linear Systems. IEEE Transactions on Automatic Control, vol. 47, no. 4, pp. 675–678, 2002.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, PRC

    Ai-Guo Wu & Guang-Ren Duan

Authors
  1. Ai-Guo Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guang-Ren Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ai-Guo Wu.

Additional information

This work was supported by the Chinese National Natural Science Foundation (No. 60374024) and Program for Changjiang Scholars and Innovative Research Team in University.

Ai-Guo Wu graduated from Harbin Institute of Technology (HIT), P. R. China, in 2002. He received the M.Sc degree from HIT in 2004. He is currently pursuing Ph.D. degree in the Center for Control Theory and Guidance Technology at HIT.

His research interests include robust control and estimation, and descriptor linear system theory.

Guang-Ren Duan graduated from the North-east Heavy Machinery Institute. He received his M.Sc degree from Heilongjiang University in 1986 and Ph.D. degree from Harbin Institute of Technology. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, China, where he became a professor of control systems theory in November 1991. Since December 2000, he has been elected Specially Empolyed Professor at Harbin Institute of Technology sponsored by the Cheung Kong Scholars Program of the Chinese government. He is now the Director of the Center for Control Theory and Guidance Technology at Harbin Institute of Technology. Dr. Duan visited the University of Hull, UK, and the University of Sheffield, UK, from December 1996 to October 1998, and was with the Queen’s University of Belfast, UK from September 1998 to September 2002.

His main research interests include robust control, eigenstructure assignment, descriptor systems, missile autopilot control and magnetic bearing control.

Dr. Duan is a Charted Engineer in the UK, a Senior Member of IEEE and a Fellow of IEE.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, AG., Duan, GR. Enhanced LMI representations for H2 performance of polytopic uncertain systems: Continuous-time case. Int J Automat Comput 3, 304–308 (2006). https://doi.org/10.1007/s11633-006-0304-5

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-006-0304-5

Keywords

Search

Navigation