International Journal of Control, Automation, and Systems

  • 제5권1호
  • /
  • Pages.86-92
  • /
  • 2007
  • /
  • 1598-6446(pISSN)
  • /
  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

On D-admissibility Conditions of Singular Systems

  • Gao, Lixin (Institute of Operations Research and Control Sciences, Wenzhou University) ;
  • Chen, Wenhai (Institute of Operations Research and Control Sciences, Wenzhou University)
  • 발행 : 2007.02.28
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we first establish $D_L$-admissibility and $D_R$-admissibility conditions for singular systems. The admissibility conditions expressed as Lyapunov type inequalities extend the existed results of normal systems to singular systems. As special cases the admissibility conditions of the continuous-time and the discrete-time singular systems can be obtained directly. The results established in this paper can be applied to solve the problems of eigenvalue assignment, regional pole-placement and robust control etc.

키워드

참고문헌

  1. L. Dai, Singular Control Systems, Lecture Notes in Control and Information Sciences, vol. 118, Springer-Verlag, New York, 1989
  2. C. Lin, J. Lam, J. Wang, and G.-H. Yang, 'Analysis on robust stability for interval descriptor systems,' Systems & Control Letters, vol. 42, pp. 267-278, 2001 https://doi.org/10.1016/S0167-6911(00)00096-7
  3. S. Xue and C. Yang, 'Stabilization of discretetime singular systems: A matrix inequalities approach,' Automatica, vol. 35, pp. 1613-1617, 1999 https://doi.org/10.1016/S0005-1098(99)00061-8
  4. Q. Zhang, W. Liu, and D. Hill, 'A Lyapunov approach to analysis of discrete singular systems,' Systems & Control Letters, vol. 45, pp. 237-247, 2002 https://doi.org/10.1016/S0167-6911(01)00184-0
  5. E. Fridman and U. Shaked, 'A Descriptor system approach to $H^{\infty}$ control of linear timedelay systems,' IEEE Trans. on Automatic Control, vol. 47, no. 2, pp. 253-270, 2002 https://doi.org/10.1109/9.983353
  6. S. Xue, C. Yang, Y. Niu, and J. Lam, 'Robust stabilization for uncertain discrete singular systems,' Automatica, vol. 37, pp.769-774, 2001 https://doi.org/10.1016/S0005-1098(01)00013-9
  7. D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou, 'A new robust D-stability condition for real convex polytopic uncertainty,' Systems & Control Letters, vol. 40, pp. 21-30, 2000 https://doi.org/10.1016/S0167-6911(99)00119-X
  8. M. Chilali, P. Gahinet, and P. Apkarian, 'Robust pole placement in LMI regions,' IEEE Trans. on Automatic Control, vol. 44, pp. 2257-2270, 1999 https://doi.org/10.1109/9.811208
  9. S. Gutman and E. I. Jury, 'A general theory for matrix root clustering in subregions of the complex plan,' IEEE Trans. on Automatic Control, vol. 26, pp. 853-863, 1981 https://doi.org/10.1109/TAC.1981.1102764
  10. X. Chen and K. Zhou, 'Fast parallel- frequencysweeping algorithms for robust D-stability margin,' IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications, vol. 50, no. 3, pp. 418-428, 2003 https://doi.org/10.1109/TCSI.2003.808843
  11. R. Yua and D. Wang, 'Structural properties and poles assignability of LTI singular systems under output feedback,' Automatica, vol. 39, pp. 685- 692, 2003 https://doi.org/10.1016/S0005-1098(02)00283-2
  12. T. Stykel, 'Stability and inertia theorems for generalized Lyapunov equations,' Linear Algebra and its Applications, vol. 355, no. 1-3, pp. 297-314, 2002 https://doi.org/10.1016/S0024-3795(02)00354-3
  13. J. Y. Ishihara and M. H. Terra, 'On the Lyapunov theorem for singular systems,' IEEE Trans. on Automatic Control, vol. 47, no. 11, pp. 1926-1930, November 2000
  14. J. C. Geromel, M. C. De Oliveira, and L. Hsu, 'LMI characterization of structural and robust stability,' Linear Algebra and its Applications, vol. 285, pp. 68-80, 1998
  15. M. C. De Oliveira, J. C. Geromel, and L. Hsu, 'LMI characterization of structural and robust stability: The discrete-time case,' Linear Algebra and its Applica-tions, vol. 296, pp. 27-38, 1999 https://doi.org/10.1016/S0024-3795(99)00086-5
  16. S. P. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994
  17. X. Huang and B. Huang, 'An BMI approach towards single and simultaneous admissible stabilization of continuous-time descriptor systems via static output feedback,' Dynamics of Continuous, Discrete and Impulse Systems Series B: Applications & Algorithms, vol. 9, pp. 71-83, 2002