Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays

Access Full Text

Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

© The Institution of Engineering and Technology
Published

The problems of delay-dependent robust stability and stabilisation for a class of uncertain two-dimensional (2-D) discrete systems with time-varying delays described by the second Fornasini–Marchesini local state space (FM LSS) model are investigated in this study. By employing improved free-weighting matrix approach, delay-dependent stability criterion for the nominal 2-D state-delayed system is first obtained and formulated in terms of linear matrix inequalities (LMIs); and then, a stabilisation design criterion using static state feedback controller is derived based on the stability result. Since the design criterion is not expressed strictly in terms of LMI, an improved cone complementary linearisation algorithm is employed to solve the non-convex feasibility problem. Furthermore, the stability and stabilisation results are extended to robust stability and stabilisation of the uncertain 2-D state-delayed system. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed method.

Inspec keywords: linear matrix inequalities; uncertain systems; stability; robust control; state feedback; linearisation techniques; delays; discrete systems

Other keywords: linear matrix inequalities; cone complementary linearisation algorithm; free-weighting matrix approach; time-varying delays; uncertain systems; delay-dependent robust stability; stabilisation; static state feedback control; nonconvex feasibility problem; 2D discrete systems; Fornasini-Marchesini local state space model

Subjects: Discrete control systems; Algebra; Distributed parameter control systems; Stability in control theory

References

    1. 1)
      • X.M. Zhang , Q.L. Han . Delay-dependent robust H∞ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality. IEEE Trans. Circuits Syst. II , 12 , 1466 - 1470
    2. 2)
      • S. Boyd , L.E. Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequality in system and control theory.
    3. 3)
      • Y. He , Q.G. Wang , L. Xie , C. Lin . Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control , 2 , 293 - 299
    4. 4)
      • H. Gao , T. Chen . New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control , 2 , 328 - 333
    5. 5)
      • H.L. Xu , Y. Zou , J.W. Lu , S.Y. Xu . Robust H∞ control for a class of uncertain nonlinear two-dimensional systems with state delays. J. Franklin Inst. , 7 , 877 - 891
    6. 6)
      • E. Fornasini . A note on output feedback stabilizability of multivariable 2-D systems. Syst. Control Lett. , 1 , 45 - 50
    7. 7)
      • She, J.H., Zhou, L., Wu, M., He, Y.: `State-observer based two-dimensional robust repetitive control', Proc. European Control Conf., August 2009, Budapest, Hungary, p. 1517–1522.
    8. 8)
      • H.D. Tuan , P. Apkarian , T.Q. Nguyen , T. Narikiyo . Robust mixed H2/H∞ filtering of 2-D systems. IEEE Trans. Signal Process. , 7 , 1759 - 1771
    9. 9)
      • J.P. Guiver , N.K. Bose . (1985) Multidimensional systems theory: progress, directions and open problems.
    10. 10)
      • Y.S. Moon , P. Park , W.H. Kwon , Y.S. Lee . Delay-dependent robust stabilisation of uncertain state-delayed systems. Int. J. Control , 14 , 1447 - 1455
    11. 11)
      • W.S. Lu . On a Lyapunov approach to stability analysis of 2-D digital filters. IEEE Trans. Circuits Syst. I , 10 , 665 - 669
    12. 12)
      • H.L. Xu , S.Y. Xu , J. Lam . Positive real control for 2-D discrete delayed systems via output feedback controllers. J. Comput. Appl. Math. , 1 , 87 - 97
    13. 13)
      • W. Paszke , J. Lam , K. Galkowski , S.Y. Xu , Z.P. Lin . Robust stability and stabilisation of 2D discrete state-delayed systems. Syst. Control Lett. , 277 - 291
    14. 14)
      • C. Du , L. Xie . Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach. IEEE Trans. Circuits Syst. I , 11 , 1371 - 1374
    15. 15)
      • J.M. Xu , L. Yu . H∞ control of 2-D discrete state delay systems. Int. J. Control, Autom. Syst. , 4 , 516 - 523
    16. 16)
      • E. Fridman , U. Shaked . Stability and guaranteed cost control of uncertain discrete delay systems. Int. J. Control , 4 , 235 - 246
    17. 17)
      • S.F. Chen , I.K. Fong . Delay-dependent robust H∞ filtering for uncertain 2-D state-delayed systems. Signal Process. , 11 , 2659 - 2672
    18. 18)
      • L. Xu , H. Park , G. Regensburger . (2006) Applications of Gröbner bases in synthesis of multidimensional control systems, Gröbner bases in control theory and signal processing.
    19. 19)
      • J.M. Xu , L. Yu . Delay-dependent H∞ control for 2-D discrete state delay systems in the second FM model. Multidimens. Syst. Signal Process. , 4 , 333 - 349
    20. 20)
      • L. Xu , O. Saito , K. Abe . Output feedback stabilizability and stabilisation algorithms for 2-D systems. Multidimens. Syst. Signal Process. , 1 , 41 - 60
    21. 21)
      • E.L. Ghaoui , F. Oustry , M. AitRami . A cone complementarity linearization algorithms for static output feedback and related problems. IEEE Trans. Autom. Control , 8 , 1171 - 1176
    22. 22)
      • Y. He , M. Wu , G.P. Liu , J.H. She . Output feedback stabilisation for a discrete-time system with a time-varying delay. IEEE Trans. Autom. Control , 10 , 2372 - 2377
    23. 23)
      • Paszke, W., Lam, J., Galkowski, K., Xu, S.Y., Kummert, A.: `Delay-dependent stability condition for uncertain linear 2-D state-delayed systems', Proc. 45th IEEE Conf. on Decision and Control, December 2006, San Diego, CA, USA, p. 2783–2788.
    24. 24)
      • T. Liu . Stability analysis of linear 2-D systems. Signal Process. , 8 , 2078 - 2084
    25. 25)
      • H. Fan , C. Wen . Adaptive control of a class of 2-D discrete systems. IEEE Trans. Circuits Syst. I , 1 , 166 - 172
    26. 26)
      • D. Peng , X. Guan . Output feedback H∞ control for 2-D state-delayed systems. Circuits Systems Signal Process. , 1 , 147 - 167
    27. 27)
      • I.R. Petersen , C.V. Hollot . A Riccati equation approach to the stabilization of uncertain linear systems. Automatica , 4 , 397 - 411
    28. 28)
      • S.G. Tzafestas . (1986) Multidimensional systems: techniques and applications.
    29. 29)
      • D. Peng , X. Guan . H∞ filtering of 2-D discrete state-delayed systems. Multidimens. Syst. Signal Process. , 3 , 265 - 274
    30. 30)
      • M. Wu , Y. He , J.H. She , G.P. Liu . Delay-dependent criteria for robust stability of time-varying delay systems. Automatica , 8 , 1435 - 1439
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2009.0284
Loading

Related content

content/journals/10.1049/iet-cta.2009.0284
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading