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, Control Applications, (CCA) Intelligent Control, (ISIC), 2009 IEEE, St. Petersburg, Russia, pp. 1009–1014.
  2. Anderson, R.J. and Spong, M.W. (1989). Bilateral control of teleoperators with time delay, IEEE Transactions on Automatic Control34(1): 494–501.10.1109/9.24201
  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, International Journal of Applied Mathematics and Computer Science22(2): 339–351, DOI: 10.2478/v10006-012-0025-6.10.2478/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, Proceedings of the IEEE94(1): 1306–1324.10.1109/JPROC.2006.876930
  5. Bellman, R. and Cooke, K. (1963). Differential-Difference Equations, Academic Press, New York, NY.10.1063/1.3050672
  6. Boyd, S., Ghaoui, L.E., Feron, E. and Belakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Vol. 15, SIAM, Philadelphia, PA.10.1137/1.9781611970777
  7. Cao, Y.Y. and Frank, P.M. (2001). Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models, Fuzzy Sets and Systems124(2): 213–229.10.1016/S0165-0114(00)00120-2
  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, Fuzzy Sets and Systems148(3): 395–410.10.1016/j.fss.2004.02.001
  9. Chen, B., Lin, C., Liu, X. and Tong, S. (2007a). Guaranteed cost control of T–S fuzzy systems with input delay, International Journal of Robust Nonlinear Control18(1): 1230–1256.10.1002/rnc.1271
  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, Fuzzy Sets and Systems158(20): 2251–2267.10.1016/j.fss.2007.04.012
  11. Chen, B. and Liu, X. (2005). Fuzzy guaranteed cost control for nonlinear systems with time-varying delay, IEEE Transactions on Fuzzy Systems13(2): 238–249.10.1109/TFUZZ.2004.840131
  12. Cheong, Niculescu, S.-I., Annaswamy, A. and Srinivasan, A. (2007). Synchronization control for physics-based collaborative virtual environments with shared haptics, Advanced Robotics21(1): 1001–1029.10.1163/156855307781035628
  13. Chiu, C.-S. and Chiang, T.-S. (2011). Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays, Journal of Systems and Control Engineering225(7): 993–1004.10.1177/0959651811394504
  14. Duda, J. (2012). A Lyapunov functional for a system with a time-varying delay, International Journal of Applied Mathematics and Computer Science22(2): 327–337, DOI: 10.2478/v10006-012-0024-7.10.2478/v10006-012-0024-7
  15. El’sgol’ts, L.E. (1966). Introduction to the Theory of Differential Equations with Deviating Arguments, Holden-Day, San Francisco, CA.
  16. Fee (1998). Twin Rotor MIMO System. Advanced Teaching Manual 1, 33-007-4M5.
  17. Gahinet, P., Nemirovski, A., Laub, A.J. and Chilali, M. (1995). LMI Control Toolbox, MathWorks, Natick, MA.
  18. Gassara, H., El-Hajjaji, A. and Chaabane, M. (2010). Delay-dependent H-infinite exponential stabilization of T–S fuzzy systems with interval time-varying delay, Proceeding of the 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, pp. 4281–4286.
  19. Gassaraa, A., El Hajjajia, A., Kchaoub, M. and Chaabaneb, M. (2014). Observer based (q,v,r)-α-dissipative control for TS fuzzy descriptor systems with time delay, Journal of the Franklin Institute351(1): 187–206.10.1016/j.jfranklin.2013.07.015
  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, 2012 9th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), DF, México, pp. 1–6.
  21. Gopalsamy, K. (1992). Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer, Norwell, MA.10.1007/978-94-015-7920-9
  22. Gu, K., Kharotonov, V. and Chen, J. (2003). Stability of Time Delay Systems, Birkhauser, Basel.10.1007/978-1-4612-0039-0
  23. Hahn, W. (1967). Stability of Motion, Springer-Verlag, Berlin.10.1007/978-3-642-50085-5
  24. Kabakov, I. (1946). Concerning the control process for the steam pleasure, Inzhenernii Sbornik2(1): 27–76.
  25. Kang, Q. and Wang, W. (2010). Guaranteed cost control for T–S fuzzy systems with time-varying delays, Journal of Control Theory and Applications8(4): 413–417.10.1007/s11768-010-9017-y
  26. Kelly, F.P. (2001). Mathematical modelling of the internet, in B. Engquist and W. Schmid (Eds.), Mathematics Unlimited—2001 and Beyond, Vol. 1, Springer-Verlag, Berlin, pp. 685–702.10.1007/978-3-642-56478-9_35
  27. Kharitonov, V. and Hinrichsen, D. (2004). Exponential estimates for time delay systems, Systems & Control Letters53(1): 395–405.10.1016/j.sysconle.2004.05.016
  28. Krasovskii, N. (1956). On the application of the second method of Lyapunov for equations with time delays, Prikladnaya Matematika i Mekhanika20(3): 315–327.
  29. La Salle, J. and Lefschetz, S. (1961). Stability by Lyapunov’s Direct Method: With Applications, Academic Press, London.
  30. Li, J., Li, J. and Xia, Z. (2011). Delay-dependent generalized H2 control for discrete T–S fuzzy large-scale stochastic systems with mixed delays, International Journal of Applied Mathematics and Computer Science21(4): 585–603, DOI: 10.2478/v10006-011-0046-6.10.2478/v10006-011-0046-6
  31. Lin, C., Wang, Q., Lee, T.H. and Chen, B. (2007). Observer-based h control for T–S fuzzy systems with time delay: Delay-dependent design method, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics34(4): 1030–1038.10.1109/TSMCB.2007.891542
  32. Lin, C., Wang, Q., Lee, T.H. and He, Y. (1991). LMI Approach to Analysis and Control of Takagi–Sugeno Fuzzy Systems with Time-Delay, 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, International Journal of Systems Science1(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, American Control Conference (ACC), Montreal, Canada, pp. 5658–5663.
  35. Mondie, S. and Kharitonov, V. (2005). Exponential estimates for retarded time-delay systems: An LMI approach, IEEE Transactions on Automatic Control50(2): 268–273.10.1109/TAC.2004.841916
  36. Murray, R.M. (Ed.) (2003). Control in an Information Rich World: Report of the Panel on Future Directions in Control, SIAM, Philadelphia, PA.10.1137/1.9780898718010
  37. Neimark, J.I. (1973). D-decomposition of spaces of quasi-polynomials, American Mathematical Society Translations102(2): 95–131.10.1090/trans2/102/05
  38. Nejjari, F., Rotondo, D., Puig, V. and Innocenti, M. (2011). LPV modelling and control of a twin rotor MIMO system, 19th Mediterranean Conference on Control Automation (MED), 2011, Corfu, Greece, 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, in I. Queinnec et al. (Eds.), Biology and Control Theory: Current Challenges, Lecture Notes in Control and Information Sciences, Vol. 317, Springer Verlag, Berlin/Heidelberg, pp. 217–259.10.1007/978-3-540-71988-5_10
  40. Oliveira, M. and Skelton, R. (2001). Stability tests for constrained linear systems, in S.Q.R. Moheimani (Ed.), Perspectives in Robust Control, Lecture Notes in Control and Information Sciences, Vol. 268, Springer-Verlag, Berlin, pp. 241–257.10.1007/BFb0110624
  41. Pratap, B. and Purwar, S. (2010). Neural network observer for twin rotor MIMO system: An LMI based approach, 2010 International Conference on Modelling, Identification and Control (ICMIC), Okayama, Japan, 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, Journal of Intelligent and Robotic Systems74(1): 69–84.10.1007/s10846-013-9946-z
  43. Razumikhin, B. (1956). On stability of systems with a delay, Prikladnaya Matematika i Mekhanika20(1): 500–512.
  44. Speich, E. and Rose, J. (2004). Medical Robotics, 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, IEEE Transactions on Systems Man and Cybernetics15(1): 116–132.10.1109/TSMC.1985.6313399
  46. Tanaka, K. and Sugeno, M. (1990). Stability analysis of fuzzy systems using Lyapunov’s direct method, NAFIPS’90, Kanazawa, Japan, pp. 133–136.
  47. Tanaka, K. and Wang, H. (2001). Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequality Approach, John Wiley & Sons, New York, NY.10.1002/0471224596
  48. Taniguchi, T., Tanaka, K. and Wang, H. (2001). Model construction, rule reduction and robust compensation for generalized form of Takagi–Sugeno fuzzy systems, IEEE Transactions on Fuzzy Systems9(2): 525–537.10.1109/91.940966
  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, IEEE Transactions on Fuzzy Systems18(5): 893–905.10.1109/TFUZZ.2010.2051447
  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, International Journal of Applied Mathematics and Computer Science22(4): 921–927, DOI: 10.2478/v10006-012-0068-8.10.2478/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, IEEE Transactions on Fuzzy Systems9(2): 324–332.10.1109/91.919253
  52. Tzypkin, J. (1946). Stability of systems with delayed feedback, Automatic and Remote Control7(2): 107–129.
  53. Wang, H., Tanaka, K. and Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems4(1): 14–23.10.1109/91.481841
  54. Wang, Z., Ho, D. and Liu, X. (2004). A note on the robust stability of uncertain stochastic fuzzy systems with time-delays, IEEE Transactions on System, Man, and Cybernetics A34(4): 570–576.10.1109/TSMCA.2004.826296
  55. Yu, L. and Chu, J. (1999). An LMI approach to guaranteed cost control of linear uncertain time-delay systems, Automatica35(1): 1155–1159.10.1016/S0005-1098(99)00007-2
  56. Zhang, B., Lam, J., Xu, S. and Shu, Z. (2009). Robust stabilization of uncertain T–S fuzzy time-delay systems with exponential estimates, Fuzzy Sets and Systems160(12): 1720–1737.10.1016/j.fss.2008.10.015
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.