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Delay compensation of discrete-time linear systems by nested prediction

Delay compensation of discrete-time linear systems by nested prediction

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In this study, the authors study the input delay compensation problem for discrete-time linear systems with both state and input delays. Under the assumption that the original time-delay system without input delay can be stabilised by state feedback, a nested predictor feedback controller is established to predict the future states such that the arbitrarily large yet exactly known input delay in the original system is completely compensated. Consequently, it is shown that the closed-loop system consisting of the original time-delay system and the nested prediction feedback controller is asymptotically stable. Under an additional assumption, an explicit nested predictor feedback controller without involving any nested summations is also established. Finally, two numerical examples are carried out to illustrate the obtained theoretical results.

References

    1. 1)
      • 1. Fridman, E.: ‘A refined input delay approach to sampled-data control’, Automatica, 2010, 46, (2), pp. 421427.
    2. 2)
      • 2. Gu, K., Chen, V.L., Kharitonov, J.: ‘Stability of time-delay systems’ (Birkhäuser, Boston, MA, 2003).
    3. 3)
      • 3. Hale, J.K.: ‘Theory of functional differential equations’ (Springer, New York, 1977).
    4. 4)
      • 4. Zhang, J., Shi, P., Xia, Y.: ‘Fuzzy delay compensation control for T–S fuzzy systems over network’, IEEE Trans. Cybern., 2013, 43, (1), pp. 259268.
    5. 5)
      • 5. Xia, Y., Liu, G.P., Shi, P., et al.: ‘Robust delay-dependent sliding mode control for uncertain timedelay systems’, Int. J. Robust Nonlinear Control, 2008, 18, (11), pp. 11421161.
    6. 6)
      • 6. Zhang, H., Zhang, D., Xie, L.: ‘An innovation approach to H prediction with applications to systems with delayed measurements’, Automatica, 2004, 40, (7), pp. 12531261.
    7. 7)
      • 7. Chen, J., Latchman, H.A.: ‘Frequency sweeping tests for stability independent of delay’, IEEE Trans. Autom. Control, 1995, 40, (9), pp. 16401645.
    8. 8)
      • 8. Gu, K., Niculescu, S.I.: ‘Additional dynamics in transformed time-delay systems’, IEEE Trans. Autom. Control, 2000, 45, (3), pp. 572575.
    9. 9)
      • 9. Zhou, B, Egorov, A.V.: ‘Razumikhin and Krasovskii stability theorems for time-varying time-delay systems’, Automatica, 2016, 71, pp. 281291.
    10. 10)
      • 10. Chen, W.-H., Zheng, W.X.: ‘Exponential stability of nonlinear time-delay systems with delayed impulse effects’, Automatica, 2011, 47, (5), pp. 10751083.
    11. 11)
      • 11. Chen, W.-H., Zheng, W.X.: ‘Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays’, Automatica, 2009, 45, pp. 14811488.
    12. 12)
      • 12. Wang, Y.-E., Sun, X.-M., Wu, B.: ‘Lyapunov–Krasovskii functionals for input-to-state stability of switched non-linear systems with time-varying input delay’, IET Control Theory Appl., 2015, 9, (11), pp. 17171722.
    13. 13)
      • 13. Zhang, B., Zheng, W.X., Xu, S.: ‘Delay-dependent passivity and passification for uncertain Markovian jump systems with time-varying delays’, Int. J. Robust Nonlinear Control, 2012, 22, (16), pp. 18371852.
    14. 14)
      • 14. Zhuang, G., Song, G., Xu, S.: ‘H filtering for Markovian jump delay systems with parameter uncertainties and limited communication capacity’, IET Control Theory Appl., 2014, 8, (14), pp. 13371353.
    15. 15)
      • 15. Chen, Y., Fei, S., Gu, Z., et al.: ‘New mixed-delay-dependent robust stability conditions for uncertain linear neutral systems’, IET Control Theory Appl., 2014, 8, (8), pp. 606613.
    16. 16)
      • 16. Cong, S.: ‘On exponential stability conditions of linear neutral stochastic differential systems with time-varying delay’, Int. J. Robust Nonlinear Control, 2013, 23, (11), pp. 12651276.
    17. 17)
      • 17. Ding, L., He, Y., Wu, M., et al.: ‘Improved mixed-delay-dependent asymptotic stability criteria for neutral systems’, IET Control Theory Appl., 2015, 9, (14), pp. 21802187.
    18. 18)
      • 18. Wu, M., He, Y., She, J.-H.: ‘New delay-dependent stability criteria and stabilizing method for neutral systems’, IEEE Trans. Autom. Control, 2004, 49, (12), pp. 22662271.
    19. 19)
      • 19. Cao, J., Wang, J.: ‘Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays’, Neural Netw., 2004, 17, (3), pp. 379390.
    20. 20)
      • 20. Huang, T., Chan, A., Huang, Y., et al.: ‘Stability of Cohen–Grossberg neural networks with time-varying delays’, Neural Netw., 2007, 20, pp. 868873.
    21. 21)
      • 21. Huang, T., Li, C., Duan, S., et al.: ‘Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects’, IEEE Trans. Neural Netw. Learn. Syst., 2012, 23, (6), pp. 866875.
    22. 22)
      • 22. Lam, J., Xu, S., Ho, D., et al.: ‘On global asymptotic stability for a class of delayed neural networks’, Int. J. Circuit Theory Appl., 2012, 40, (11), pp. 11651174.
    23. 23)
      • 23. Yang, X., Cao, J., Yang, Z.: ‘Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller’, SIAM J. Control Optim., 2013, 51, (5), pp. 34863510.
    24. 24)
      • 24. Yang, X., Cao, J., Long, Y., Rui, W.: ‘Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations’, IEEE Trans. Neural Netw., 2010, 21, (10), pp. 16561667.
    25. 25)
      • 25. Zeng, Z., Huang, T., Zheng, W.X.: ‘Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function’, IEEE Trans. Neural Netw., 2010, 21, (8), pp. 13711377.
    26. 26)
      • 26. Xiong, J., Lam, J.: ‘Stabilization of linear systems over networks with bounded packet loss’, Automatica, 2007, 43, pp. 8087.
    27. 27)
      • 27. Xu, S., Lam, J., Zou, Y.: ‘Improved conditions on delaydependent robust stability and stabilization of uncertain discrete time-delay systems’, Asian J. Control, 2005, 7, (3), pp. 344348.
    28. 28)
      • 28. Zhang, J., Lin, Y., Feng, G.: ‘Design of memoryless output feedback controller of discrete-time systems with input delay’, IET Control Theory Appl., 2015, 9, (8), pp. 12051212.
    29. 29)
      • 29. Zhou, B., Li, Z., Lin, Z.: ‘Stabilization of discrete-time systems with multiple actuator delays and saturations’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2013, 60, (2), pp. 389400.
    30. 30)
      • 30. Peng, D., Hua, C.: ‘Improved approach to delay-dependent stability and stabilisation of two-dimensional discrete-time systems with interval time-varying delays’, IET Control Theory Appl., 2015, 9, (12), pp. 18391846.
    31. 31)
      • 31. Zhou, B., Lam, J., Duan, G.-R.: ‘Full delayed state feedback pole assignment of discrete-time time-delay systems’, Optim. Control Appl. Methods, 2010, 31, (2), pp. 155169.
    32. 32)
      • 32. Zhang, J., Zhang, H., Luo, Y., et al: ‘Model-free optimal control design for a class of linear discrete-time systems with multiple delays using adaptive dynamic programming’, Neurocomputing, 2014, 135, pp. 163170.
    33. 33)
      • 33. Zhou, B.: ‘Observer based output feedback control of discrete-time linear systems with input and output delays’, Int. J. Control, 2014, 87, (11), pp. 22522272.
    34. 34)
      • 34. Zhou, B., Li, Z., Lin, Z.: ‘Observer based output feedback control of linear systems with input and output delays’, Automatica, 2013, 49, (7), pp. 20392052.
    35. 35)
      • 35. Zhou, B.: ‘Input delay compensation of linear systems with both state and input delays by nested prediction’, Automatica, 2014, 50, (5), pp. 14341443.
    36. 36)
      • 36. Zhou, B., Liu, Q.: ‘Input delay compensation for neutral-type time-delay systems’. 2015, Submitted for publication.
    37. 37)
      • 37. Zhou, B.: ‘Input delay compensation of linear systems with both state and input delays by adding integrators’, Syst. Control Lett., 2015, 82, pp. 5163.
    38. 38)
      • 38. Kharitonov, V.L.: ‘An extension of the prediction scheme to the case of systems with both input and state delay’, Automatica, 2014, 50, (1), pp. 211217.
    39. 39)
      • 39. Sobel, K.M., Shapiro, E.Y.: ‘A design methodology for pitch pointing flight control systems’, J. Guid. Control Dyn., 1985, 8, (2), pp. 181187.
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