International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Stability of Time Delay Systems Using Numerical Computation of Argument Principles

  • Published : 2003.03.01
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Abstract

This paper proposes a new numerical method to check the stability of a general class of time delay systems. The proposed method checks whether there are characteristic roots whose real values are nonnegative through two steps. Firstly, rectangular bounds of characteristic roots whose real values are nonnegative are computed. Secondly, the existence of roots inside the bounds are checked using the numerical computation of argument principles. An adaptive discretization is proposed for the numerical computation of argument principles.

Keywords

References

  1. Int. J. Contrl. v.47 no.4 LQ regulator design method for system with delay based on spectral devomposition of the hamiltonian E. Shimemura;K. Uchida;T. Kubo https://doi.org/10.1080/00207178808906068
  2. Proc. of 38th IEEE Conference on Decision and Control Receding horizon control for state delayed system with its stability W. H. Kwon;J. W. Kang;Y. S. Moon
  3. SIAM J. Control v.13 no.1 Stability and the infinite-time quadratic cost problem for linear hereditary differential systems M. C. Delfour;C. McCalla;S. K. Mitter https://doi.org/10.1137/0313004
  4. IEEE Trans. on Automat. Contr. v.40 no.6 On computing the maximal delay intervals for stability of linear delay systems J. Chen https://doi.org/10.1109/9.388690
  5. IEE Proceedings v.131 no.1 Simplified analytic stability test for systems with commensurate time delays D. Hertz;E. I. Jury;E. Zeheb
  6. IEEE Trans. on Automat. Contr. v.47 no.5 An exact method for the stability analysis of time-delayed linaer time-invarinat(LTI) systems N. Olgac;R. Sipahi https://doi.org/10.1109/TAC.2002.1000275
  7. SIAM J. Sci Stat. Comput. v.8 no.3 Computation of eigenvalues associated with functional differential equations A. Manitius;H. Tran;G. Payre;R. Roy https://doi.org/10.1137/0908032
  8. Feedback Systems; Input-Output Properties C. A. Desoer;M. Vidyasagar
  9. Automatica v.29 no.1 The complex structured singular value A. Packard;J. Doyle https://doi.org/10.1016/0005-1098(93)90175-S
  10. IEEE Trans. on Automat. Contr. v.AC-34 no.4 Stability of x(t)=Ax(t)+Bx(t-Τ) T. Mori;H. Kokame
  11. Linear Matrix Inequalities in System and Control Theory S. Boyd;L. E. Ghaoui;E. Feron;V. Balakrishnan
  12. Computational Methods for LInear Control Systems P. H. Petkov;N. D. Christov;M. M. Konstantinov
  13. Complex Variables and Applications R. V. Churchill
  14. J. of Computational Physics v.45 Solution of equatons involving analytic functions M. P. Carpentier;A. F. D. Santos https://doi.org/10.1016/0021-9991(82)90117-6
  15. Proc. of CDC Delay-dependent stability of lienar systems with delayed state: an LMI approach S. I. Niculescu;A. T. Neto;J. M. Dion;L. Dugard