Skip to main content
Have a personal or library account? Click to login
Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations Cover

Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

Open Access
|Dec 2015

References

  1. Ahmed, Q., Bhatti, A. and Iqbal, S. (2009). Robust decoupling control design for twin rotor system using Hadamard weights,, pp. 1009–1014.
  2. Anderson, R.J. and Spong, M.W. (1989). Bilateral control of teleoperators with time delay,(1): 494–501.
  3. Balasubramaniam, P., Lakshmanan, S. and Rakkiyappan, R. (2012). LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties,(2): 339–351, DOI: 10.2478/v10006-012-0025-6.
  4. Beard, W.B., McLain, T.W., Nelson, D.B., Kingston, D. and Johanson, D. (2006). Decentralized cooperative aerial surveillance using fixed-wing miniature UAVs,(1): 1306–1324.
  5. Bellman, R. and Cooke, K. (1963)., Academic Press, New York, NY.
  6. Boyd, S., Ghaoui, L.E., Feron, E. and Belakrishnan, V. (1994)., Vol. 15, SIAM, Philadelphia, PA.
  7. Cao, Y.Y. and Frank, P.M. (2001). Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models,(2): 213–229.
  8. Chang, Y.C., Chen, S., Su, S. and Lee, T. (2004). Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach,(3): 395–410.
  9. Chen, B., Lin, C., Liu, X. and Tong, S. (2007a). Guaranteed cost control of T–S fuzzy systems with input delay,(1): 1230–1256.
  10. Chen, B., Liu, X.and Tong, S. and Lin, C. (2007b). Guaranteed cost control of T–S fuzzy systems with state and input delays,(20): 2251–2267.
  11. Chen, B. and Liu, X. (2005). Fuzzy guaranteed cost control for nonlinear systems with time-varying delay,(2): 238–249.
  12. Cheong, Niculescu, S.-I., Annaswamy, A. and Srinivasan, A. (2007). Synchronization control for physics-based collaborative virtual environments with shared haptics,(1): 1001–1029.
  13. Chiu, C.-S. and Chiang, T.-S. (2011). Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays,(7): 993–1004.
  14. Duda, J. (2012). A Lyapunov functional for a system with a time-varying delay,(2): 327–337, DOI: 10.2478/v10006-012-0024-7.
  15. El’sgol’ts, L.E. (1966)., Holden-Day, San Francisco, CA.
  16. Fee (1998).33-007-4M5.
  17. Gahinet, P., Nemirovski, A., Laub, A.J. and Chilali, M. (1995)., MathWorks, Natick, MA.
  18. Gassara, H., El-Hajjaji, A. and Chaabane, M. (2010). Delay-dependent-infinite exponential stabilization of T–S fuzzy systems with interval time-varying delay,, pp. 4281–4286.
  19. Gassaraa, A., El Hajjajia, A., Kchaoub, M. and Chaabaneb, M. (2014). Observer based (q,v,r)--dissipative control for TS fuzzy descriptor systems with time delay,(1): 187–206.
  20. Gonzalez, T., Rivera, P. and Bernal, M. (2012). Nonlinear control for plants with partial information via Takagi–Sugeno models: An application on the twin rotor MIMO system,, pp. 1–6.
  21. Gopalsamy, K. (1992)., Kluwer, Norwell, MA.
  22. Gu, K., Kharotonov, V. and Chen, J. (2003)., Birkhauser, Basel.
  23. Hahn, W. (1967)., Springer-Verlag, Berlin.
  24. Kabakov, I. (1946). Concerning the control process for the steam pleasure,(1): 27–76.
  25. Kang, Q. and Wang, W. (2010). Guaranteed cost control for T–S fuzzy systems with time-varying delays,(4): 413–417.
  26. Kelly, F.P. (2001). Mathematical modelling of the internet,B. Engquist and W. Schmid (Eds.),, Vol. 1, Springer-Verlag, Berlin, pp. 685–702.
  27. Kharitonov, V. and Hinrichsen, D. (2004). Exponential estimates for time delay systems,(1): 395–405.
  28. Krasovskii, N. (1956). On the application of the second method of Lyapunov for equations with time delays,(3): 315–327.
  29. La Salle, J. and Lefschetz, S. (1961)., Academic Press, London.
  30. Li, J., Li, J. and Xia, Z. (2011). Delay-dependent generalizedcontrol for discrete T–S fuzzy large-scale stochastic systems with mixed delays,(4): 585–603, DOI: 10.2478/v10006-011-0046-6.
  31. Lin, C., Wang, Q., Lee, T.H. and Chen, B. (2007). Observer-basedcontrol for T–S fuzzy systems with time delay: Delay-dependent design method,(4): 1030–1038.
  32. Lin, C., Wang, Q., Lee, T.H. and He, Y. (1991)., Prentice Hall, New York, NY.
  33. Liu, H., Shi, P., Karimi, H. and Chadli, M. (2014). Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay,(1): 1–12.
  34. Marquez Rubio, J.F., del Muro Cuéllar, B. and Sename, O. (2012). Control of delayed recycling systems with an unstable pole at forward path,, pp. 5658–5663.
  35. Mondie, S. and Kharitonov, V. (2005). Exponential estimates for retarded time-delay systems: An LMI approach,(2): 268–273.
  36. Murray, R.M. (Ed.) (2003)., SIAM, Philadelphia, PA.
  37. Neimark, J.I. (1973). D-decomposition of spaces of quasi-polynomials,(2): 95–131.
  38. Nejjari, F., Rotondo, D., Puig, V. and Innocenti, M. (2011). LPV modelling and control of a twin rotor MIMO system,, pp. 1082–1087.
  39. Niculescu, S.-I., Morărescu, C., Michiels, W. and Gu, K. (2007). Geometric ideas in the stability analysis of delay models in biosciences,I. Queinnec(Eds.),, Lecture Notes in Control and Information Sciences, Vol. 317, Springer Verlag, Berlin/Heidelberg, pp. 217–259.
  40. Oliveira, M. and Skelton, R. (2001). Stability tests for constrained linear systems,S.Q.R. Moheimani (Ed.),, Lecture Notes in Control and Information Sciences, Vol. 268, Springer-Verlag, Berlin, pp. 241–257.
  41. Pratap, B. and Purwar, S. (2010). Neural network observer for twin rotor MIMO system: An LMI based approach,pp. 539–544.
  42. Ramírez, A., Espinoza, E.S., García, L.R., Mondié, S., García, A. and Lozano, R. (2014). Stability analysis of a vision-based UAV controller,(1): 69–84.
  43. Razumikhin, B. (1956). On stability of systems with a delay,(1): 500–512.
  44. Speich, E. and Rose, J. (2004)., Prentice Hall, Marcel Dekker, New York, NY.
  45. Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control,(1): 116–132.
  46. Tanaka, K. and Sugeno, M. (1990). Stability analysis of fuzzy systems using Lyapunov’s direct method,, pp. 133–136.
  47. Tanaka, K. and Wang, H. (2001)., John Wiley & Sons, New York, NY.
  48. Taniguchi, T., Tanaka, K. and Wang, H. (2001). Model construction, rule reduction and robust compensation for generalized form of Takagi–Sugeno fuzzy systems,(2): 525–537.
  49. Tao, C., Taur, J.-S., Chang, Y.-H. and Chang, C.-W. (2010). A novel fuzzy-sliding and fuzzy-integral-sliding controller for the twin-rotor multi-input-multi-output system,(5): 893–905.
  50. Thuan, M.V., Phat, V.N. and Trinh, H. (2012). Observer-based controller design of time-delay systems with an interval time-varying delay,(4): 921–927, DOI: 10.2478/v10006-012-0068-8.
  51. Tuan, H., Apkarian, P., Narikiyo, T. and Yamamoto, Y. (2001). Parameterized linear matrix inequality techniques in fuzzy control system design,(2): 324–332.
  52. Tzypkin, J. (1946). Stability of systems with delayed feedback,(2): 107–129.
  53. Wang, H., Tanaka, K. and Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues,(1): 14–23.
  54. Wang, Z., Ho, D. and Liu, X. (2004). A note on the robust stability of uncertain stochastic fuzzy systems with time-delays,(4): 570–576.
  55. Yu, L. and Chu, J. (1999). An LMI approach to guaranteed cost control of linear uncertain time-delay systems,(1): 1155–1159.
  56. Zhang, B., Lam, J., Xu, S. and Shu, Z. (2009). Robust stabilization of uncertain T–S fuzzy time-delay systems with exponential estimates,(12): 1720–1737.
DOI: https://doi.org/10.1515/amcs-2015-0058 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 815 - 826
Submitted on: Aug 2, 2014
Published on: Dec 30, 2015
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2015 Máximo Ramírez, Raúl Villafuerte, Temoatzin González, Miguel Bernal, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.