The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Robust Non-fragile Guaranteed Cost Control for Uncertain Descriptor Systems with State Delay

시간지연을 가지는 변수 불확실성 특이시스템의 비약성 강인 보장비용 제어

  • 김종해 (선문대학교 전자공학부)
  • Published : 2007.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers robust and non-fragile guaranteed cost controller design method for descriptor systems with parameter uncertainties and time delay, and static state feedback controller with gain variations. The existence condition of controller, the design method of controller, the upper bound to minimize guaranteed cost function, and the measure of non-fragility in controller are proposed using linear matrix inequality (LMI) technique, which can be solved efficiently by convex optimization. Therefore, the presented robust and non-fragile guaranteed cost controller guarantees the asymptotic stability and non-fragility of the closed loop systems in spite of parameter uncertainties, time delay, and controller fragility.

Keywords

References

  1. M. S. Mahmoud and N. F. Al-Muthairi, 'Quadratic stabilization of continuous time systems with state delay and norm-bounded time-varying uncertainties,' IEEE Trans. on Automatic Control, vol. 39, no. 10, pp. 2135-2139, 1994 https://doi.org/10.1109/9.328812
  2. H. H. Choi and M. J. Chung, 'Memoryless Roo controller design for linear systems with delayed state and control,' Automatica, vol. 31, pp. 917-919, 1995 https://doi.org/10.1016/0005-1098(95)00001-D
  3. J. H. Lee, S. W. Kim, and W. H. Kwon, 'Memoryless $H_{\infty}$ controllers for state delayed systems,' IEEE Trans. on Automatic Control, vol. 39, pp. 159-162, 1994 https://doi.org/10.1109/9.273356
  4. J. H. Kim, E. T. Jeung and H. B. Park, 'Robust control for parameter uncertain delay systems in state and control input,' Automatica, vol. 32, pp. 1337-1339, 1996 https://doi.org/10.1016/0005-1098(96)00074-X
  5. S. S. L. Chang and T. K. C. Peng, 'Adaptive guaranteed cost control of systems with uncertain parameters,' IEEE Trans. on Automatic Control, vol. 17, pp. 474-483, 1972 https://doi.org/10.1109/TAC.1972.1100037
  6. I. R. Petersen and D. C. McFarlane, 'Optimal guaranteed cost control and filtering for uncertain linear systems,' IEEE Trans. on Automatic Control, vol. 39, pp. 1971-1977, 1994 https://doi.org/10.1109/9.317138
  7. I. R. Petersen, 'Guaranteed cost LQG control of uncertain linear systems,' IEE Proc.-D, vol. 142, pp.95-102, 1995 https://doi.org/10.1049/ip-cta:19951732
  8. P. L. D. Peres, J. C. Geromel, and S. R. Souza, '$H_{\infty}$ guaranteed cost control for uncertain continuous-time linear systems,' Systems and Control Letters, vol. 20, pp.413-418, 1993 https://doi.org/10.1016/0167-6911(93)90102-C
  9. Y. S. Lee, O. K. Kwon, and W. H. Kwon, 'Delay-dependent guaranteed cost control for uncertain state delayed systems,' International Journal of Control, Automation, and Systems, vol. 3, pp. 524-532, 2005
  10. L. Yu and J. Chu, 'An LMI approach to guaranteed cost control of linear uncertain time delay system,' Automatica, vol. 35, pp. 1155-1159, 1999 https://doi.org/10.1016/S0005-1098(99)00007-2
  11. J. H. Kim, 'Guaranteed cost control of parameter uncertain systems with time delay,' Transaction on Control, Automation, and Systems Engineering, vol. 2, pp. 19-23, 2000
  12. I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, '$H_{\infty}$ control for descriptor systems: A matrix inequalities approach,' Automatica, vol. 33, pp. 669-673, 1997 https://doi.org/10.1016/S0005-1098(96)00193-8
  13. K. Takaba, N. Morihara, T. Katayama, 'A general Lyapunov theorem for descriptor system,' System and Control Lett., vol. 24, pp, 49-51, 1995 https://doi.org/10.1016/0167-6911(94)00041-S
  14. P. Dorato, C. T. Abdallah, and D. Famularo, 'On the design of non -fragile compensators via symbolic quantifier elimination,' World Automation Congress, pp. 1098-1105, 1997
  15. L. H. Keel and S. P. Bhattacharyya, 'Robust, fragile, or optimal,' IEEE Trans. on Automatic Control, vol. 42, pp. 1098-1105, 1997 https://doi.org/10.1109/9.618239
  16. W. M. Haddad and J. R. Corrado, 'Non-fragile controller design via quadratic Lyapunov bounds,' Proc. IEEE Control Decision on Conference, pp. 2678-2683, 1997
  17. D. Famularo, C T. Abdallah, A. Jadbabaie, P. Dorato, and W. M. Haddad, 'Robust non-fragile LQ controllers: The static state feedback case,' Proc. American Control Conference, pp. 1109-1113, 1998
  18. P. Dorato, 'Non-fragile controller design: An overview,' Proc. American Control Conference, pp. 2829-2831, 1998
  19. A. Jadbabie, C. T. Abdalah, D. Famularo, and P. Dorato, 'Robust non-fragile and optimal controller design via linear matrix inequalities,' Proc. American Control Conference, pp. 2842-2846, 1998
  20. S. S. Hung and T. T. Lee, 'Memoryless tt: controller for singular systems with delayed state and control,' Journal of the Franklin Institute, vol. 336, pp. 911-923, 1999 https://doi.org/10.1016/S0016-0032(99)00018-6
  21. J. H. Kim, 'New design method on memory less H 00 control for singular systems with delayed state and control using LMI,' Journal of the Franklin Institute, vol. 342, pp. 321-327, 2005 https://doi.org/10.1016/j.jfranklin.2004.11.006
  22. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Mathworks Inc., 1995