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LMI based control design for linear systems with distributed time delays

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.
Rocznik
Strony
217--231
Opis fizyczny
Bibliogr. 21 poz., rys., wzory
Twórcy
autor
autor
  • Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia, anna.filasova@tuke.sk
Bibliografia
  • [1] D. Boyd, L. El Ghaoui, E. Peron and V. Balakrishnan: Linear Matrix Inequalities in System and Control Theory. Philadelphia, SIAM Society for Industrial and Applied Mathematics, 1994.
  • [2] Z. Feng and J. Lam: Integral partitioning approach to stability analysis and stabilization of distributed time delay systems. Preprints of the 18th IFAC World Congress, Milano, Italy, (2011), 5094-5099.
  • [3] Z. Feng and J. Lam: Integral partitioning approach to robust stabilization for uncertain distributed time delay systems. Int. J. of Robust and Nonlinear Control, 22 (2012), 676-689.
  • [4] Y. A. Fiagbedzi and A. E. Pearson: A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica, 23(3), (1987), 311-326.
  • [5] P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali: LMI Control Toolbox User's Guide. Natick, The MathWorks, Inc., 1995.
  • [6] D. Gontkovič and R. Fónod: State control design for linear systems with distributed time delay. Proc. of the 10th IEEE Jubilee Int. Symp. on Applied Machine Intelligence and Informatics SAMI 2012, Herĺany, Slovakia, (2012), 97-101.
  • [7] F. Gouaisbaut and D. Peaucelle: Delay-dependent stability analysis of linear time delay systems. Proc. of the 6th IFAC Workshop on Time Delay System TDS'06, LAquila, Italy, (2006).
  • [8] K. Gu: An improved stability criterion for systems with distributed delays. Int. J. of Robust and Nonlinear Control, 13 (2003), 819-831.
  • [9] G. Herrmann, M. C. Turner and I. Postlethwaite: Linear matrix inequalities in control. Mathematical Methods for Robust and Nonlinear Control. Berlin, Springer-Verlag, 2007, 123-142.
  • [10] N. N. Krasovskii: On the application of Lyapunov's second method for equations with time delays. Prikladnaja matematika i mechanika, 20 (1956), 315-327, (in Russian).
  • [11] N. N. Krasovskii: Stability of Motion: Application of Lyapunov's Second Method to Differential Systems and Equations with Delay. Standford, Standford University Press, 1963.
  • [12] D. Krokavec and A. Filasová: Discrete-Time Systems. Košice, Elfa, 2006, (in Slovak).
  • [13] D. Krokavec and A. Filasová: Exponential stability of networked control systems with network-induced random delays. Archives of Control Sciences, 20(2), (2010), 165-186.
  • [14] S. I. Niculescu, E. I. Veriest, L. Dugard and J. M. Dion: Stability and robust stability of time-delay systems: A guided tour. Stability and Control of Time-delay Systems. Berlin, Springer-Verlag, 1998, 1-71.
  • [15] D. Peaucelle, D. Henrion, Y. Labit and K. Taitz: User's Guide for SeDuMi Interface 1.04. Toulouse, LAAS-CNRS, 2002.
  • [16] U. Shaked, I. Yaesh and C. E. De Souza: Bounded real criteria for linear time systems with state-delay. IEEE Trans. on Automatic Control, 43 (1998), 1116-1121.
  • [17] Y. S. Suh, H. J. Kang and Y. S. Ro: Stability condition of distributed delay systems based on an analytic solution to Lyapunov functional equations. Asian J. of Control, 8 (2006), 91-96.
  • [18] J. Sun, J. Chen, G. Liu and D. Rees: On robust stability of uncertain neutral systems with discrete and distributed delays. Proc. of American Control Conference, St. Louis, MO, USA, (2009), 5469-5473.
  • [19] M. Wu, Y. He, J. J. She and G. P. Liu: Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 40 (2004), 1435-1439.
  • [20] F. Zheng and P. M. Frank: Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica, 38 (2002), 487-497.
  • [21] Q. C. Zhong: Robust Control of Time-delay Systems. London, Sprin-ger-Verlag, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0098-0014
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