Design of Robust Guaranteed Cost State Feedback Controller for Uncertain Discrete-time Singular Systems using LMI

선형행렬부등식을 이용한 불확실성 이산시간 특이시스템의 강인 보장비용 상태궤환 제어기 설계

  • 김종해 (선문대학교 전자공학부)
  • Published : 2008.08.01

Abstract

In this paper, we consider the design method of robust guaranteed cost controller for discrete-time singular systems with norm-bounded time-varying parameter uncertainty. In order to get the optimum(minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) approach. The sufficient condition for the existence of controller and the upper bound of guaranteed cost function are proposed in terms of strict LMIs without decompositions of system matrices. Numerical examples are provided to show the validity of the presented method.

Keywords

References

  1. L. Dai, Singular Control Systems, Lecture Notes in control and Information Science, Springer: New York, 1989
  2. 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
  3. H. S. Wang, C. F. Yung, and F. R. Chang, "Bounded real lemma and $H_{\infty}$ control for descriptor systems," IEE Proc.-Control Theory & Appl., vol. 145, pp. 316-322, 1998
  4. K. L. Hsiung, "Lyapunov inequality and bounded real lemma for discrete-time descriptor systems," Proc. of the 37th CDC, pp. 289-290, 1998
  5. S. Xu and C. Yang, "$H_{\infty}$ state feedback control for discrete singular systems," IEEE Trans. on Automatic Control, vol. 45, pp. 1405-1409, 2000 https://doi.org/10.1109/9.867074
  6. G. Zhang and Y. Jia, "New results on discrete-time bounded real lemma for singular systems: strict matrix inequality conditions," Proc. of the American Control Conference, pp. 634-638, 2002
  7. S. Xu and C. Yang, "Stabilization of discrete-time singular systems: a matrix inequalities approach," Automatica, vol. 35, pp. 1613-1617, 1999 https://doi.org/10.1016/S0005-1098(99)00061-8
  8. S. Xu, 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
  9. S. Wo, Y. Zou, M. Sheng, and S. Xu, "Robust control for discrete-time singular large-scale systems with parameter uncertainty," Journal of the Franklin Institute, vol. 344, pp. 97-106, 2007 https://doi.org/10.1016/j.jfranklin.2006.08.005
  10. 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
  11. J. H. Kim, "Robust guaranteed cost control of discrete-time uncertain systems with time delays," IEICE Trans. Fundamentals, vol. E84-A, pp. 1-5, 2001
  12. P. Shi, E. K. Boukas, Y. Shi, and R. K. Agarwal, "Optimal guaranteed cost control of uncertain discrete time-delay systems," Journal of Computational and Applied Mathematics, vol. 157, pp. 435-451, 2003 https://doi.org/10.1016/S0377-0427(03)00433-3
  13. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies 15 in Applied Mathematics, 1994
  14. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Works Inc., 1995