The Transactions of the Korean Institute of Electrical Engineers D (대한전기학회논문지:시스템및제어부문D)

The Korean Institute of Electrical Engineers (대한전기학회)
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On Guaranteed Cost Control of Uncertain Neutral Systems

섭동을 갖는 뉴트럴 시스템의 성능보장 안정화에 관하여

  • 박주현 (영남대학교 전기정보공학과)
  • Published : 2003.03.01
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Abstract

In this paper, we consider the robust guaranteed cost control problem for a class of uncertain neutral systems with given quadratic cost functions. The uncertainty is assumed to be norm-bounded and time-varying. The goal in this study is to design the memoryless state feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound lot all admissible uncertainty. Some criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the Lyapunov second method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.

Keywords

References

  1. J. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Spring-Verlag, New York, 1993
  2. V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992
  3. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Boston, 1992
  4. D.Y. Khusainov and E.V. Yun'kova, Investigation of the stability of linear systems of neutral type by the Lyapunov function method, Differentsialnye Uravneniya, 24 (1988), 613-621
  5. J. X. Kuang, J. X. Xiang, and H. J. Tian, The asymptotic stability if one-parameter methods for neutral differential equations, BIT, 34 (1994), 400-408 https://doi.org/10.1007/BF01935649
  6. L.M. Li, Stability of Iinear neutral delay-differential systems, Bulletin of Australian Mathematical Society, 38 (1988), 339-344 https://doi.org/10.1017/S0004972700027684
  7. G.D. Hu and G.D. Hu, Some stability criteria of neutral delay-differential systems, Applied Mathematics and Computation, 80 (1996), 257-271 https://doi.org/10.1016/0096-3003(95)00301-0
  8. J.H. Park and S. Won, A note on stability of neutral delay-differential systems, Journal of The Franklin Institute, 336 (1999), 543-548 https://doi.org/10.1016/S0016-0032(98)00040-4
  9. J.H. Park and S. Won, Asymptotic stability of neutral systems with multiple delays, Journal of Optimization Theory and Applications, 103 (1999), 187-200 https://doi.org/10.1023/A:1021781602182
  10. E.N. Chukwu, Stability and Time-Optimal Control of Hereditary Systems, Academic Press, New York, 1992
  11. T. J. Tarn, T. Yang, X. Zeng, and C. Guo, Periodic output feedback stabilization of neutral systems, IEEE Transactions on Automatic Control, 41 (1996), 511-521 https://doi.org/10.1109/9.489272
  12. Y. A. Fiagbedziu, Feedback stabilization of neutral systems via the transformation technique, International Journal of Control, 59 (1994), 1579-1589 https://doi.org/10.1080/00207179408923147
  13. W.B. Ma, N. Adachi, and T. Amemiya, Delay independent stabilization of uncertain linear systems of neutral type, Journal of Optimization Theory and Application, 84 (1995), 393-405 https://doi.org/10.1007/BF02192121
  14. S.S.L. Chang and T.K.C. Peng, Adaptive guaranteed cost control of systems with uncertain parameters, IEEE Transaction on Automatic Control, 17 (1972), 474-483 https://doi.org/10.1109/TAC.1972.1100037
  15. I.R. Petersen, D.C. McFarlane, and M.A. Rotea, Optimal guaranteed cost control of discrete-time uncertain linear systems, International Journal of Robust and Nonlinear Control, 8 (1998), 649-657 https://doi.org/10.1002/(SICI)1099-1239(19980715)8:8<649::AID-RNC334>3.0.CO;2-6
  16. L. Yu, and J. Chu, An LMI approach to guaranteed cost control of linear uncertain time-delay systems, Automatica, 35 (1999), 1155-1159 https://doi.org/10.1016/S0005-1098(99)00007-2
  17. P. Khargonekar, I.R. Petersen, and K. Zhou, Robust stabilization of nucertain linera systems: Quadratic stability and $H_{\infty}$ control theory, IEEE Transaction on Automatic Control, 35 (1990), 356-361 https://doi.org/10.1109/9.50357
  18. B. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, 1994
  19. P. Gahinet, A. Nemirovski, A. Laub, and M.Chilali, LMI Control Toolbox User's Guide, The Mathworks, Natick, Massachustts, 1995