Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Static output feedback stabilization for systems with time-varying delay based on a matrix transformation method

基于一种矩阵变换方法的线性时变时滞系统的静态输出反馈镇定

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper is concerned with the problem of static output feedback stabilization for linear systems with time-varying delay. A novel controller design is proposed based on a matrix transformation method with a new equation condition, which can solve the controller gain more easily and avoid complicated calculations of the non-linear matrix inequality. Then, the corresponding criteria can be obtained by combining the matrix transformation method and the ideas of non-uniformly dividing delay interval, which can guarantee the asymptotic stability of the closed-loop systems and calculate the satisfactory controller gain. Finally, two numerical examples are provided to verify the effectiveness of the proposed design scheme.

创新点

提出了一种基于矩阵变换方法的输出反馈控制器设计方案, 这个方案可以更加方便的求解出控制器的增益, 从而避免了由于求解非线性矩阵不等式所带来的复杂运算. 通过结合非一致划分时滞区间方法, 提出的矩阵变换方法可以更好的处理带有时变时滞的线性系统的输出反馈镇定问题, 保证其闭环系统的稳定性. 通过理论证明, 分析了提出方法相对于现有方法的相互关系, 定性地说明该方法的优势.

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

Similar content being viewed by others

References

  1. Niculescu S I, Abdallah C T. Delay effects on static output feedback stabilization. In: Proceedings of the 39th IEEE Conference on Decision and Control (CDC 2000), Sydney, 2000. 2811–2816

    Google Scholar 

  2. Marquez-Martinez L A, Moog C H. Input-output feedback linearization of time-delay systems. IEEE Trans Autom Control, 2004, 49: 781–785

    Article  MathSciNet  Google Scholar 

  3. Kharitonov V L, Niculescu S I, Moreno J, et al. Static output feedback stabilization: necessary conditions for multiple delay controllers. IEEE Trans Autom Control, 2005, 50: 82–86

    Article  MathSciNet  Google Scholar 

  4. Li X D, Xian B, Diao C, et al. Output feedback control of hypersonic vehicles based on neural network and high gain observer. Sci China Inf Sci, 2011, 54: 429–447

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen P N, Qin H S, Wang Y, et al. Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control. Sci China Inf Sci, 2012, 55: 200–213

    Article  MATH  MathSciNet  Google Scholar 

  6. Yan X G, Spurgeon S K, Edwards C. Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback. Automatica, 2013, 49: 633–641

    Article  MATH  MathSciNet  Google Scholar 

  7. Deshpande P, Menon P P, Edwards C. Delayed static output feedback control of a network of double integrator agents. Automatica, 2013, 49: 3498–3501

    Article  MathSciNet  Google Scholar 

  8. Zhu S Q, Meng M, Zhang C H. Exponential stability for positive systems with bounded time-varying delays and static output feedback stabilization. J Franklin Inst, 2013, 350: 617–636

    Article  MATH  MathSciNet  Google Scholar 

  9. Tong S C, Li Y M. Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems. Sci China Inf Sci, 2014, 57: 012204

    Article  MathSciNet  Google Scholar 

  10. Gao Y, Wu H N, Wang J W, et al. Feedback control design with vibration suppression for flexible air-breathing hypersonic vehicles. Sci China Inf Sci, 2014, 57: 032204

    Google Scholar 

  11. Li G C, Song S J, Wu C. Subgradient-based feedback neural networks for non-differentiable convex optimization problems. Sci China Ser-F: Inf Sci, 2006, 49: 421–435

    Article  MATH  MathSciNet  Google Scholar 

  12. Matiakis T, Hirche S, Buss M. Control of networked systems using the scattering transformation matiakis. IEEE Trans Control Syst Technol, 2009, 17: 60–67

    Article  Google Scholar 

  13. Zou Y Y, Li S Y. Receding horizon estimation to networked control systems with multirate scheme. Sci China Inf Sci, 2009, 52: 1103–1112

    Article  MATH  MathSciNet  Google Scholar 

  14. Hao F, Zhao X. Linear matrix inequality approach to static output-feedback stabilisation of discrete-time networked control systems. IET Proc Control Theory Appl, 2010, 4: 1211–1221

    Article  MathSciNet  Google Scholar 

  15. Wang N, Zhang T W, Xu J Q. Formation control for networked spacecraft in deep space: with or without communication delays and with switching topology. Sci China Inf Sci, 2011, 54: 469–481

    Article  MathSciNet  Google Scholar 

  16. Liu K, Fridman E. Networked-based stabilization via discontinuous Lyapunov functionals. Int J Robust Nonlinear Contr, 2012, 22: 420–436

    Article  MATH  MathSciNet  Google Scholar 

  17. Crusius C A R, Trofino A. Sufficient LMI conditions for output feedback control problems. IEEE Trans Autom Control, 1999, 44: 1053–1057

    Article  MATH  MathSciNet  Google Scholar 

  18. Apkarian P, Tuan H D, Bernussou J. Continuous-time analysis, eigenstructure assignment, and H 2 synthesis with enhanced linear matrix inequalities (LMI) characterizations. IEEE Trans Autom Control, 2001, 46: 1941–1946

    Article  MATH  MathSciNet  Google Scholar 

  19. Dong J X, Yang G H. Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties. IEEE Trans Autom Control, 2007, 52: 1930–1936

    Article  MathSciNet  Google Scholar 

  20. Chen K F, Feng I K. Stability analysis and output-feedback stabilisation of discrete-time systems with an interval time-varying state delay. IET Proc Control Theory Appl, 2010, 4: 563–572

    Article  Google Scholar 

  21. Zhang B, Wang X, Cai K Y. Approximate trajectory tracking of input-disturbed PVTOL aircraft with delayed attitude measurements. Int J Robust Nonlinear Contr, 2010, 20: 1610–1621

    Article  Google Scholar 

  22. Gao H J, Lam J, Wang C H, et al. Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proc Control Theory Appl, 2004, 151: 691–698

    Article  Google Scholar 

  23. Liu X G, Martin R R, Wu M, et al. Delay-dependent robust stabilisation of discrete-time systems with time-varying delay. IEE Proc Control Theory Appl, 2006, 153: 689–702

    Article  MathSciNet  Google Scholar 

  24. He Y, Wu M, Liu G P, et al. Output feedback stabilization for a discrete-time system with a time-varying delay. IEEE Trans Autom Control, 2008, 53: 2372–2377

    Article  MathSciNet  Google Scholar 

  25. Shu Z, Lam J, Xiong J. Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach. Automatica, 2010, 46: 687–694

    Article  MATH  MathSciNet  Google Scholar 

  26. Du B Z, Lam J, Shu Z. Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica, 2010, 46: 2000–2007

    Article  MATH  MathSciNet  Google Scholar 

  27. Zhang H G, Liu Z W, Huang G B, et al. Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw, 2010, 21: 91–106

    Article  Google Scholar 

  28. Zhang H G, Liu Z W. Stability analysis for linear delayed systems via an optimally dividing delay interval approach. Automatica, 2011, 47: 2126–2129

    Article  MATH  Google Scholar 

  29. Gu K Q, Kharitonov V, Chen J. Stability of Time-Delay Systems. Cambridge: Birkhauser, 2003

    Google Scholar 

  30. Liu Z W, Zhang H G. Delay-dependent stability for systems with fast-varying neutral-type delay via a PTVD compensation. Acta Automat Sinica, 2010, 36: 147–152

    MathSciNet  Google Scholar 

  31. Shao H Y. New delay-dependent stability criteria for systems with interval delay. Automatica, 2009, 45: 744–749

    Article  MATH  Google Scholar 

  32. Zhang H G, Liu Z W, Huang G B. Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique. IEEE Trans Syst Man Cybern Part B-Cybern, 2010, 40: 1480–1491

    Article  Google Scholar 

  33. Liu Z W, Zhang H G, Zhang Q L. Novel compensation-based non-fragile H ∞ control for uncertain neutral systems with time-varying delays. Int J Syst Sci, 2012, 43: 961–971

    Article  Google Scholar 

  34. Nelder J A, Mead R. A simplex method for function minimization. Comput J, 1965, 7: 308–313

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    ZhenWei Liu, HuaGuang Zhang & QiuYe Sun

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110004, China

    ZhenWei Liu, HuaGuang Zhang & QiuYe Sun

Authors
  1. ZhenWei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. HuaGuang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. QiuYe Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to HuaGuang Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Zhang, H. & Sun, Q. Static output feedback stabilization for systems with time-varying delay based on a matrix transformation method. Sci. China Inf. Sci. 58, 1–13 (2015). https://doi.org/10.1007/s11432-014-5205-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-014-5205-6

Keywords

关键词

Search

Navigation