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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 141))

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Abstract

This chapter deals with the stabilization of a nominal and uncertain time-delay systems using state feedback control law.

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Notes

  1. 1.

    refer sub-section 2.3.2, Theorem 2.5.

References

  1. J.C. Shen, B.S. Chen, F.C. Kung, Memoryless stabilization of uncertain dynamic delay system: Ricatti equation approach. IEEE Trans. Autom. Control 36, 638–640 (1991)

    Article  Google Scholar 

  2. S. Phoojaruenchanachai, K. Furuta, Memoryless stabilization of uncertain linear system including time-varying sate delay. IEEE Trans. Autom. Control 37, 1022–1026 (1992)

    Article  MATH  Google Scholar 

  3. M.S. Mahmoud, N.F. Al-muthairi, Quadratic stabilization of continuous time system with the state delay and norm bounded uncertainties. IEEE Trans. Autom. Control 39, 2135–2139 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Trinh, M. Aldeen, Stabilization of uncertain dynamic delay system by memoryless state feedback controllers. Int. J. Control 56, 1525–1542 (1994)

    Article  MATH  Google Scholar 

  5. A. Trinh, M. Aldeen, “Robust stabilization and disturbance attenuation for uncertain time-delay systems,” in European Control conference, 1993, pp. 0 – 0

    Google Scholar 

  6. X. Li, C.E. de Souza, Criteria for robust stability and stabilization of uncertain linear systems with state delays. Automatica 33, 1657–1662 (1997)

    Article  MathSciNet  Google Scholar 

  7. X. Li, C.E. de Souza, Delay-dependent robust stability and stabilization of uncertain linear delay system:a linear matrix inequality approach. IEEE Trans. Autom. Control 42, 1144–1148 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Y.Y. Cao, Y.X. Sun, C. Cheng, Delay-dependent robust stabilizion of uncertain systems with multiple state delays. IEEE Trans. Autom. Control 43, 1608–1612 (1998)

    Article  MATH  Google Scholar 

  9. Y.S. Moon, P. Park, W.H. Kwon, Y.S. Lee, Delay-dependent robust stabilization of uncertain state delayed system. Int. J. control 74, 1447–1455 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Fridman, U. Shaked, An improved stabilization method for linear time-delay system. IEEE Trans. Autom. Control 47, 1931–1937 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. E. Fridman, U. Shaked, Parameter dependent stability and stabilization of uncertain time-delay systems. IEEE Trans. Autom. Control 48, 861–866 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. M.N.A. Parlakci, Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time-delay system. Int. J. Robust Nonlinear Control 16, 599–636 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. M.N.A. Parlakci, Delay-dependent stability and state feedback stabilization criterion for linear time delay system, in International Conference on Modeling and Simulation, Coimbator-Vol.2, 2007, pp. 963 – 968

    Google Scholar 

  14. M.N.A. Parlakci, Delay-dependent stability and \(H_{\infty }\) control: Constant and time-varying delays. Int. J. Control 76, 48–60 (2003)

    Article  MathSciNet  Google Scholar 

  15. K. Gu, S.I. Niculescu, Additional dynamics in transformed time-dealy systems. IEEE Trans. Autom. Control 45, 00–00 (2000)

    Google Scholar 

  16. E. Ghaoui, F. Oustry, M.A. Rami, A cone-complementary linearization algorithm for static output feedback and related problems. IEEE Trans. Autom. Control 42, 1171–1176 (1997)

    Article  MATH  Google Scholar 

  17. P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI control toolbox users guide (Mathworks, Cambridge, 1995)

    Google Scholar 

  18. E. Fridamn, U. Shaked, A descriptor system approach to \(H_{\infty }\) control of linear time-delay systems. IEEE Trans. Autom. Control 47, 253–270 (2002)

    Article  MathSciNet  Google Scholar 

  19. S. Xu, J. Lam, Y. Zou, Delay-dependent guaranteed cost control for uncertain system with state and input delays. IEE Proc. Control Theory Appl. 153, 307–313 (2006)

    Article  MathSciNet  Google Scholar 

  20. T. Li, L. Guo, Y. Zhang, Delay-range-dependent robust stability and stabilization for uncertain systems with time-varying delay. Int. J. Robust Nonlinear Control 18, 1372–1387 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. C.E. de Souza, X. Li, Delay-dependent robust \(H_{\infty }\) control of uncertain linear state-delayed systems. Automatica 35, 1313–1321 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. V. Suplin, E. Fridman, U. Shaked, \(H_{\infty }\) control of linear uncertain time-delay systems-a projection approach. IEEE Trans. Autom. Control 31, 680–685 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Dey, S. Ghosh, G. Ray, A. Rakshit, State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality appraoch. Numer. Linear Algebra with Appl. 18(3), 351–361 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Dey, G. Ray, S. Ghosh, A. Rakshit, Stability analysis for contious system with additive time-varying delays: A less conservative result. Appl. Mathematics Comput. 215, 3740–3745 (2010)

    MathSciNet  MATH  Google Scholar 

  25. S. Niculescu, A.T. Neto, J.M. Dion, L. Dugard, Roust stability and stabilization of uncertain linear systems with state delay: Multiple delay case \({(I)}\), in IFAC symposium on Robust control Design, 1994

    Google Scholar 

  26. J.W. Ko, P.G. Park, Delay-dependent robust stabilization for systems with time-varying delays. Int. J. Control Autom. Sys. 7, 711–722 (2009)

    Article  Google Scholar 

  27. D.D. Siljak, D.M. Stipanovic, A.I. Zecevic, Robust decentralized turbine/governor control using linear matrix inequalities. IEEE Trans. Power Sys. 17, 715–722 (2002)

    Article  Google Scholar 

  28. P.P.K.J.C. Doyle, K. Glover, B.A. Francis, State-space solutions to the standard \(H_{2}\) and \(H_{\infty }\) control problems. IEEE Trans. Autom. Control 34, 831–927 (1989)

    Google Scholar 

  29. B.A. Francis, A course in \(H_{\infty }\) Control Theory (Springer Verlag, New York, 1987)

    Google Scholar 

  30. H.H. Choi, M.J. Chung, Observer-based \(H_{\infty }\) controller design for state delayed linear system. Automatica 32, 1073–1075 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  31. S.W.K.J.H. Lee, W.H. Kwon, Memoryless \(H_{\infty }\) controller for state delayed systems. IEEE Trans. Autom. Control 39, 159–162 (1994)

    Google Scholar 

  32. S. Niclescu, C. E. D. Souza, J. M. Dion, L. Dugard, Robust \(H_{\infty }\) memoryless control of uncertain linera systems with time-varying delay, in Proceedings of 1995 Euoropean Control Conference, Rome, 1995, pp. 1814 – 1819

    Google Scholar 

  33. M.S. Mahmoud, M. Zribi, \(H_{\infty }\) controllers for linearized time-delay systems using LMI. J. Optim. Theory and Appl. 100, 89–112 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  34. M.S. Mahmoud, M. Zribi, “Robust stabilization and \({H}_{\infty }\) controlfor uncertain linear time-delay system: An \(\text{LMI}\) approach,” in \(13^{th}\) IFAC World Congress, San Francisco, 1996, pp. 113 – 118

    Google Scholar 

  35. Y.Y. Cao, Y.X. Sun, J. Lam, Delay-dependent robust \({H}_{\infty }\) control for uncertain system with time-varying delays. IEE Proc. of CTA 145, 338–344 (1998)

    Google Scholar 

  36. X. Li, E. Fridman, U. Shaked, Robust \(H_{\infty }\) control of distributed delay systems with application to combustion control. IEEE Trans. Autom. control 46, 1930–1933 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  37. G. Ray, A.N. Prasad, G.D. Prasad, Design of robust lfc for interconnected power system based on singular value decomposition method. Electric Power Syst. Res. 37, 209–219 (1996)

    Article  Google Scholar 

  38. H. Bevrani, T. Hiyama, Robust decentralized \(\text{ PI }\) based \(\text{ LFC }\) design for time-delay system. Energy Conversion Manage. 49, 193–204 (2008)

    Article  Google Scholar 

  39. T.C. Yang, H. Cimen, Q.M. Zhu, Decentralized \(\text{ LFC }\) design based on structured singular value. IEE Proc. Generation, Transm. Distribution 145, 7–14 (1998)

    Article  Google Scholar 

  40. D. Rerkpreedapong, A. Feliachi, “Decentralized \(H_{\infty }\) load frequency control using lmi control toolbox,” in IEEE proceedings of the circuit and systems (ISCAS’03), 2003, pp. 411 – 414

    Google Scholar 

  41. D. Dotta, A.S. Silva, I.C. Decker, Wide-area measurements-based two-level control design considering signal transmission delay. IEEE Trans. Power Sys. 24, 208–216 (2009)

    Article  Google Scholar 

  42. M. Zribi, M.S. Mahmoud, M. Karkoub, T.T. Lie, \(H_{\infty }\) controller for linearized time-delay power system. IEE proc. Generation Transm. Distribution 147, 401–403 (2000)

    Article  Google Scholar 

  43. T. Ishii, G. Shirai, G. Fujita, Decentralized load frequency based on \(H_{\infty }\) control. Electr. Eng. Japan 136, 28–38 (2001)

    Article  Google Scholar 

  44. A.Y. Sivaramakrishnan, M.V. Hariharan, M.C. Srisailam, Design of variable structure load frequency controller using pole placement technique. IEEE Trans. Autom. Control 14, 487–498 (1984)

    MATH  Google Scholar 

  45. C.T. Pan, C.M. Liaw, An adaptive controller for power system \(\text{ LFC }\). IEEE Trans. Power Sys. 14, 122–128 (1989)

    Article  Google Scholar 

  46. E.A.A. Nedzad, N ERC compliant decentralized \(\text{ LFC }\) design using \(\text{ MPC }\). IEEE Power Eng. Soc. Gen. Meeting 2, 13–17 (2003)

    Google Scholar 

  47. S. Bhowmick, K. Tomsovic, A. Bose, Communication models for third party \(\text{ LFC }\). IEEE Trans. Power Sys. 19, 543–548 (2004)

    Article  Google Scholar 

  48. X. Yu, K. Tomsovic, Application of linear matrix inequalities for load frequency control with communication delay. IEEE Trans. Power Sys. 19, 1508–1515 (2004)

    Article  Google Scholar 

  49. H. Jiang, H. Cai, J.F. Dorsey, Z. Qu, Towards a globally robust decentralized control for large-scale power systems. IEEE Trans. Control Sys. Technol. 5, 309–319 (1997)

    Article  Google Scholar 

  50. G.J. Li, T.T. Lie, C.B. Soh, G.H. Yang, Decentralized \(H_{\infty }\) control for power system stability enhancement. Electr. Power and Energy Sys. 20, 453–464 (1998)

    Article  Google Scholar 

  51. R. Dey, S. Ghosh, G. Ray, A. Rakshit, \(h_\infty \) load frequency control of interconnected power system with communication delays. Electr. Power Energy Sys. 42, 672–684 (2012)

    Article  Google Scholar 

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Dey, R., Ray, G., Balas, V.E. (2018). Stabilization of Time-Delay Systems. In: Stability and Stabilization of Linear and Fuzzy Time-Delay Systems. Intelligent Systems Reference Library, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-70149-3_3

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  • DOI: https://doi.org/10.1007/978-3-319-70149-3_3

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