Browse > Article

Development of non-fragile $H_{\infty}$ controller design algorithm for singular systems  

Kim, Jong-Hae (Division of Electronic Eng., Sun Moon University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SC / v.42, no.6, 2005 , pp. 9-14 More about this Journal
Abstract
In this paper, we consider the synthesis of non-fragile $H_{\infty}$ state feedback controllers for singular systems and static state feedback controller with multiplicative uncertainty. The sufficient condition of controller existence, the design method of non-fragile $H_{\infty}$ controller, and the measure of non-fragility in controller are presented via LMI(linear matrix inequality) technique. Also, the sufficient condition can be rewritten as LMI form in terms of transformed variables through singular value decomposition, some changes of variables, and Schur complements. Therefore, the obtained non-fragile $H_{\infty}$ controller guarantees the asymptotic stability and disturbance attenuation of the closed loop singular systems within a prescribed degree. Moreover, the controller design method can be extended to the problem of robust and non-fragile $H_{\infty}$ controller design method for singular systems with parameter uncertainties. Finally, a numerical example is given to illustrate the design method.
Keywords
Singular systems; linear matrix inequality;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Dorato, P., Non fragile Controller Design: An Overview, Proceedings of the American Control Conference, Philadelphia, Pennsylvania, pp. 2829-2831, 1998   DOI
2 Keel, L.H., and Bhattacharyya, S.P., Robust, Fagile, or Optimal, IEEE Transactions on Automatic Control, Vol. 42, No.8, pp. 1098-1105, 1997   DOI   ScienceOn
3 K. Gu, '$H_{\infty}$ control of systems under norm bounded in all system matrices,' IEEE Trans. Automat. Control, vol. 39, pp. 1320-1322, 1994   DOI   ScienceOn
4 A. Rhem and F. Allgower, '$H_{\infty}$ control of descriptor systems with norm-bounded uncertainties in the system matrices,' Proc. of American Control Conference, pp. 3244-3248, 2000   DOI
5 P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Works Inc., 1995
6 K. Takaba, N. Morihara, and T. Katayama, 'A generalized Lyapunov theorem for descriptor system,' Systems and Control Lett., vol. 24, pp. 49-51, 1995.no. 3, pp. 345-357, June 1998   DOI   ScienceOn
7 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   DOI   ScienceOn
8 W. M. Haddad and J. R. Corrado, 'Resilient dynamic controller design via quadratic Lyapunov bounds,' Proc. of IEEE Conference on Decision and Control, pp. 2678-2683, 1997   DOI
9 A. Jadbabie, C. T. Abdalah, D. Famularo, and P. Dorato, 'Robust non-fragile and optimal controller design via linear matrix inequalities,' Proc. of American Control Conference, pp. 2842-2846, 1998   DOI
10 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
11 Famularo. D., Abdalah, C.T., Jadbabaie, A. Dorato, P., and Haddad, W.M., Robust Non-fragile LQ Controllers: The Static State Feedback Case, Proceedings of the American Control Conference, Philadelphia, Pennsylvania, pp. 1109- 1113, 1998   DOI