International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Robust and Non-fragile $H_{\infty}$ Control for Descriptor Systems with Parameter Uncertainties and Time Delay

  • Kim, Jong-Hae (Division of Electronic Engineering, Sun Moon University) ;
  • Oh, Do-Chang (Department Electronics & Information Engineering, Konyang University)
  • Published : 2007.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

This paper describes a robust and non-fragile $H_{\infty}$ controller design method for descriptor systems with parameter uncertainties and time delay, as well as a static state feedback controller with multiplicative uncertainty. The controller existence condition, as well as its design method, and the measure of non-fragility in the controller are proposed using linear matrix inequality(LMI) technique, which can be solved efficiently by convex optimization. Therefore, the presented robust and non-fragile $H_{\infty}$ controller guarantees the asymptotic stability and disturbance attenuation of the closed loop systems within a prescribed degree in spite of parameter uncertainties, time delay, disturbance input and controller fragility.

Keywords

References

  1. 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
  2. K. Takaba, N. Morihara, and T. Katayama, 'A generalized Lyapunov theorem for descriptor system,' System and Control Letters, vol. 24, pp. 49-51, 1995 https://doi.org/10.1016/0167-6911(94)00041-S
  3. 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
  4. W. M. Haddad and J. Corrado, 'Non-fragile controller design via quadratic Lyapunov bounds,' Proc. of IEEE Control Decision on Conference, pp. 2678-2683, 1997
  5. D. Famularo, C. T. Abdallah, A. Jadbabaie, P. Dorato, and W. M. Haddad, 'Robust non-fragile LQ controllers: The static state feedback case,' Proc. of American Control Conference, pp. 1109-1113, 1998
  6. P. Dorato, 'Non-fragile controller design: An overview,' Proc. American Control Conference, pp. 2829-2831, 1998
  7. 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
  8. P. Dorato, C. T. Abdallah, and D. Famularo, 'On the design of non-fragile compensators via symbolic quantifier elimination,' World Automation Congress, pp. 9-14, 1998
  9. H. H. Choi and M. J. Chung, 'Memoryless $H_\infty$ 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
  10. J. H. Kim and H. B. Park, '$H_\infty$ state feedback control for generalized continuous/discrete timedelay system,' Automatica, vol. 35, pp. 1443-1451, 1999 https://doi.org/10.1016/S0005-1098(99)00038-2
  11. S. S. Hung and T. T. Lee, 'Memoryless $H_\infty$ 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
  12. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Mathworks Inc., 1995