This study is concerned with the problem of output feedback fuzzy H_∞-tracking control design for nonlinear time-delay systems. Initially, a discrete-time Takagi–Sugeno (T–S) modelling approach is applied. Then a general and extended structure for the controller is assumed. Finally, a linear matrix inequality (LMI) approach is offered to find the possible solutions. The final design will result in the closed-loop stability of the system together with minimising the H_∞-tracking control norm to some reference and bounded signals. Despite the existing results which offer a set of coupled LMIs and a double step algorithm to find a possible solution, the authors' results are a single step and less conservative. Moreover, the authors let the time delay to exist both in state and input matrices of the T–S fuzzy model. Two simulation examples are given to illustrate the effectiveness of the obtained method in comparison with the existing ones.

References

1. 1)
  - 18. Wang, W.J., Lin, H.R.: ‘Fuzzy control design for the trajectory tracking on uncertain nonlinear systems’, IEEE Trans. Fuzzy Syst., 1999, 7, (1), pp. 53–62 (doi: 10.1109/91.746308).
2. 2)
  - 13. Lam, H.K., Li, H.: ‘Output-feedback tracking control for polynomial fuzzy-model-based control systems’, IEEE Trans. Ind. Electron., 2013, 60, (12), pp. 5830–5840 (doi: 10.1109/TIE.2012.2229679).
3. 3)
  - 25. Liu, Y.-J., Wang, W., Tong, S.C., et al: ‘Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters’, IEEE Trans. Syst. Man Cybern. A, Syst. Humans, 2010, 40, (1), pp. 170–184 (doi: 10.1109/TSMCA.2009.2030164).
4. 4)
  - 33. Lin, C., Wang, Q., Lee, T.H., et al: ‘LMI approach to analysis and control of Takagi–Sugeno fuzzy systems with time delay’ (Springer-Verlag, 2007, 1st edn.).
5. 5)
  - 8. Salehi, S., Shahrokhi, M.: ‘Adaptive fuzzy approach for H∞ temperature tracking control of continuous stirred tank reactors’, Control Eng. Pract., 2008, 16, pp. 1101–1108 (doi: 10.1016/j.conengprac.2007.12.005).
6. 6)
  - 5. Tanaka, K., Wang, H.O.: ‘Fuzzy control systems design and analysis: a linear matrix inequality approach’ (John Wiley & Sons, 2001, 1st edn.).
7. 7)
  - 28. Hwang, C.-L., Chiang, C.-C., Yeh, Y.-W.: ‘Adaptive fuzzy hierarchical sliding-mode control for trajectory tracking of uncertain underactuated nonlinear dynamic systems’, IEEE Trans. Fuzzy Syst., 2014, 22, (2), pp. 286–299 (doi: 10.1109/TFUZZ.2013.2253106).
8. 8)
  - 7. Huang, G.-S., Uang, H.-J.: ‘Robust adaptive PID tracking control design for uncertain spacecraft systems: a fuzzy approach’, IEEE Trans. Aerosp. Electron. Syst., 2006, 42, (4), pp. 1506–1514 (doi: 10.1109/TAES.2006.314591).
9. 9)
  - 37. Lam, H.K., Seneviratne, L.D.: ‘Tracking control of sampled–data fuzzy-model-based control systems’, IET Control Theory Appl., 2007, 3, (1), pp. 56–67 (doi: 10.1049/iet-cta:20070466).
10. 10)
  - 40. Cao, Y., Chen, X.B.: ‘An output-tracking-based discrete PID-sliding mode control for MIMO systems’, IEEE Trans. Mechatron., 2014, 19, (4), pp. 1183– 1194 (doi: 10.1109/TMECH.2013.2275743).
11. 11)
  - 14. Hung, C.-Y., Liu, P., Lian, K.-Y.: ‘Fuzzy virtual model sensorless tracking control for linear induction motors’, IEEE Trans. Cybern., 2013, 43, (3), pp. 970–981 (doi: 10.1109/TSMCB.2012.2220347).
12. 12)
  - 38. Lam, H.K.: ‘Sampled-data fuzzy-model-based control systems: stability analysis with consideration of analogue-to-digital converter and digital-to-analogue converter’, IET Control Theory Appl., 2010, 4, (7), pp. 1131–1144 (doi: 10.1049/iet-cta.2008.0599).
13. 13)
  - 15. Rojas-Ramirez, E., Benitez-Read, J.S., Rios, A.S.D.L.: ‘A stable adaptive fuzzy control scheme for tracking an optimal power profile in a research nuclear reactor’, Ann. Nucl. Energy, 2013, 58, pp. 238–245 (doi: 10.1016/j.anucene.2013.03.026).
14. 14)
  - 26. Chang, Y.-T., Chen, B.-S.: ‘A fuzzy approach for robust reference-tracking-control design of nonlinear distributed parameter time-delayed systems and its applications’, IEEE Trans. Fuzzy Syst., 2010, 18, (6), pp. 1041–1057 (doi: 10.1109/TFUZZ.2010.2058809).
15. 15)
  - 16. Liu, Y.J., Tong, S.C., Li, T.S.: ‘Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems’, Fuzzy Sets Syst., 2011, 164, (1), pp. 25–44 (doi: 10.1016/j.fss.2010.09.002).
16. 16)
  - 19. Li, T.-S., Tong, S.-C., Feng, G.: ‘A novel robust adaptive-fuzzy tracking control for a class of nonlinear multi-input/multi-output systems’, IEEE Trans. Fuzzy Syst., 2010, 18, (1), pp. 150–160 (doi: 10.1109/TFUZZ.2009.2038277).
17. 17)
  - 5. Tseng, C.S., Chen, B.S.: ‘H∞ decentralized fuzzy model reference tracking control design for nonlinear interconnected systems’, IEEE Trans. Fuzzy Syst., 2001, 9, (6), pp. 795–809 (doi: 10.1109/91.971729).
18. 18)
  - 12. Tanaka, K., Segeno, M.: ‘Stability analysis and design of fuzzy control of nonlinear systems: Stability and the design issues’, Fuzzy Sets Syst., 1992, 45, (2), pp. 135–156 (doi: 10.1016/0165-0114(92)90113-I).
19. 19)
  - 36. Kim, E., Park, C.: ‘Fuzzy disturbance observer approach to robust tracking control of nonlinear sampled systems with the guaranteed suboptimal H∞ performance’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2004, 34, (3), pp. 1574–1581 (doi: 10.1109/TSMCB.2004.825917).
20. 20)
  - 1. Sastry, S.: ‘Nonlinear systems, analysis, stability and control’ (Springer, 1999).
21. 21)
  - 9. Lin, C.-K.: ‘Fuzzy-basis-function-network-based H∞ tracking control for robotic manipulators using only position feedback’, IEEE Trans. Fuzzy Syst., 2009, 17, (5), pp. 1208–1216 (doi: 10.1109/TFUZZ.2009.2025370).
22. 22)
  - 27. Kung, C.C., Chen, T.H.: ‘H∞ tracking based adaptive fuzzy sliding mode controller design for nonlinear systems’, IET Control Theory Appl., 2007, 1, (1), pp. 82–89 (doi: 10.1049/iet-cta:20050160).
23. 23)
  - 11. Chen, B.-S., Wu, C.-H.: ‘Robust reference-tracking design method for stochastic synthetic biology systems: T–S fuzzy approach’, IEEE Trans. Fuzzy Syst., 2010, 18, (6), pp. 1144–1159 (doi: 10.1109/TFUZZ.2010.2070842).
24. 24)
  - 21. Hu, X., Wu, L., Hu, C., Gao, H.: ‘Fuzzy guaranteed cost tracking control for a flexible air-breathing hypersonic vehicle’, IET Control Theory A, 2012, 6, (9), pp. 1238–1249 (doi: 10.1049/iet-cta.2011.0065).
25. 25)
  - 42. Boyd, S., El Ghaoui, L., Feron, E., et al: ‘Linear matrix inequalities in system and control theory’ (SIAM, 1994, 1st edn.).
26. 26)
  - 18. Zhou, Q., Shi, P., Xu, S., Li, H.: ‘Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach’, IEEE Trans. Fuzzy Syst., 2013, 21, pp. 301–313 (doi: 10.1109/TFUZZ.2012.2213259).
27. 27)
  - 41. Esfahani, S.H., Sichani, A.Kh.: ‘An improvement on the problem of optimal fuzzy H∞-tracking control design for nonlinear systems’, IET Control Theory Appl., 2011, 5, (1), pp. 2179–2190 (doi: 10.1049/iet-cta.2010.0480).
28. 28)
  - 31. Tseng, C., Chen, B., Uang, H.: ‘Fuzzy tracking control design for nonlinear dynamic systems via T–S fuzzy model’, IEEE Trans. Fuzzy Syst., 2001, 9, (3), pp. 381–392 (doi: 10.1109/91.928735).
29. 29)
  - 18. Li, H.X., Tong, S.: ‘A hybrid adaptive fuzzy control for a class of nonlinear mimo systems’, IEEE Trans. Fuzzy Syst., 2003, 11, (1), pp. 24–34 (doi: 10.1109/TFUZZ.2002.806314).
30. 30)
  - 32. Lin, C., Wang, Q., Lee, T.: ‘H∞ output tracking control for nonlinear systems via T–S fuzzy model approach’, IEEE Trans. Syst. Man Cybern., 2006, 36, (2), pp. 450–457 (doi: 10.1109/TSMCB.2005.856723).
31. 31)
  - 30. Chang, Y.C.: ‘Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and H∞ approaches’, IEEE Trans. Fuzzy Syst., 2001, 9, (2), pp. 278–292 (doi: 10.1109/91.919249).
32. 32)
  - 4. Wang, H.O., Tanaka, K., Griffin, M.F.: ‘An approach to fuzzy control of nonlinear systems: stability and design issues’, IEEE Trans. Fuzzy Syst., 1996, 4, (1), pp. 14–23 (doi: 10.1109/91.481841).
33. 33)
  - 16. Chu, Z.Y., Cui, J., Sun, F.-C.: ‘Fuzzy adaptive disturbance-observer-based robust tracking control of electrically driven free-floating space manipulators’, IEEE Syst. J., 2014, 8, (2), pp. 343–352 (doi: 10.1109/JSYST.2012.2220171).
34. 34)
  - 29. Hwang, C.-L., Lin, H.-Y.: ‘A fuzzy decentralized variable structure tracking control with optimal and improved robustness designs: theory and applications’, IEEE Trans. Fuzzy Syst., 2004, 12, (5), pp. 615–630 (doi: 10.1109/TFUZZ.2004.834819).
35. 35)
  - 16. Takagi, T., Sugeno, M.: ‘Fuzzy identification of systems and its applications to modeling and control’, IEEE Trans. Syst. Man Cybern., 1985, 15, (1), pp. 116–132 (doi: 10.1109/TSMC.1985.6313399).
36. 36)
  - 17. Ying, H.: ‘Analytical analysis and feedback linearization tracking control of the general Takagi–Sugeno fuzzy dynamic systems’, IEEE Trans. Syst. Man Cybern., 1999, 29, (3), pp. 290–298 (doi: 10.1109/5326.760573).
37. 37)
  - 6. Lam, H.K., Seneviratne, L.D.: ‘LMI-based stability design of fuzzy controller for nonlinear systems’, IET Control Theory Appl., 2006, 1, (1), pp. 393–401 (doi: 10.1049/iet-cta:20060105).
38. 38)
  - 35. Tseng, C.: ‘Model reference output fuzzy tracking control design for nonlinear discrete-time systems with time-delay’, IEEE Trans. Fuzzy Syst., 2006, 14, (1), pp. 58–70 (doi: 10.1109/TFUZZ.2005.861609).
39. 39)
  - 10. Chen, C.-S.: ‘Supervisory adaptive tracking control of robot manipulators using interval type-2 TSK fuzzy logic system’, IET Control Theory Appl., 2011, 5, (15), pp. 1796–1807 (doi: 10.1049/iet-cta.2010.0703).
40. 40)
  - 39. Chiang, T.S., Liu, P.: ‘Robust output tracking control for discrete-time nonlinear systems with time-varying delay: virtual fuzzy model LMI-based approach’, Expert Syst. Appl., 2012, 39, pp. 8239–8247 (doi: 10.1016/j.eswa.2012.01.163).
41. 41)
  - 22. Liu, Y.J., Tong, S.C., Wang, W.: ‘Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems’, Fuzzy Sets Syst., 2009, 160, (1), pp. 2727–2754 (doi: 10.1016/j.fss.2008.12.016).

Improvement on the problem of output feedback fuzzy H_∞-tracking control design for non-linear discrete-time systems with state and input delay

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Improvement on the problem of output feedback fuzzy H∞-tracking control design for non-linear discrete-time systems with state and input delay

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Improvement on the problem of output feedback fuzzy H_∞-tracking control design for non-linear discrete-time systems with state and input delay