References

• 1. 1)
     • 14. Lam, J., Xu, S., Zou, Y., et al: ‘Robust output feedback stabilization for two-dimensional continuous systems in Roesser form’, Appl. Math. Lett., 2004, 17, (12), pp. 1331–1341.
  2. 2)
     • 6. Chen, S.F.: ‘Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model’, Appl. Math. Comput., 2010, 216, (9), pp. 2613–2622.
  3. 3)
     • 1. Du, C., Xie, L.: ‘H∞ control and filtering of two-dimensional systems’ (Springer, Berlin, 2002).
  4. 4)
     • 8. Singh, V.: ‘New approach to stability of 2-D discrete systems with state saturation’, Signal Process., 2012, 92, (1), pp. 240–247.
  5. 5)
     • 43. Kaczorek, T.: ‘Positive fractional 2D continuous-discrete linear systems’, Bull. Polish Acad. Sci. Tech. Sci., 2011, 59, (4), pp. 575–579.
  6. 6)
     • 26. Li, L., Sun, Y.: ‘Adaptive fuzzy control for nonlinear fractional-order uncertain systems with unknown uncertainties and external disturbance’, Entropy, 2015, 17, (8), pp. 5580–5592.
  7. 7)
     • 20. Rossikhin, Y., Shitikova, M.V.: ‘Application of fractional operators to the analysis of damped vibrations of viscoelastic single-mass systems’, J. Sound Vib., 1997, 199, (4), pp. 567–586.
  8. 8)
     • 42. Kaczorek, T.: ‘Practical stability of positive fractional 2D linear systems’, Multidimens. Syst. Signal Process., 2010, 21, (3), pp. 231–238.
  9. 9)
     • 19. Gabano, J.D., Poinot, T.: ‘Fractional modelling and identification of thermal systems’, Signal Process., 2011, 91, (3), pp. 531–541.
  10. 10)
      • 41. Kaczorek, T.: ‘Practical stability and asymptotic stability of positive fractional 2D linear systems’, Asian J. Control, 2010, 12, (2), pp. 200–207.
  11. 11)
      • 13. Benzaouia, A., Benhayoun, M., Tadeo, F.: ‘State feedback stabilization of 2-D continuous systems with delays’, Int. J. Innov. Comput. Inf. Control, 2011, 7, (2), pp. 977–988.
  12. 12)
      • 11. Kurek, J.E.: ‘Stability of nonlinear time-varying digital 2-D Fornasini–Marchesini system’, Multidimens. Syst. Signal Process., 2014, 25, (1), pp. 235–244.
  13. 13)
      • 24. Lakshmikantham, V., Leela, S., Sambandham, M.: ‘Lyapunov theory for fractional differential equations’, Commun. Appl. Anal., 2008, 12, (4), pp. 365–376.
  14. 14)
      • 36. Chen, L., He, Y., Chai, Y., et al: ‘New results on stability and stabilization of a class of nonlinear fractional-order systems’, Nonlinear Dyn., 2014, 75, (4), pp. 633–641.
  15. 15)
      • 5. Paszke, W., Lam, J., Galkowski, K., et al: ‘Robust stability and stabilisation of 2D discrete state-delayed systems’, Syst. Control Lett., 2004, 51, (3), pp. 277–291.
  16. 16)
      • 21. Sejdic, E., Djurovic, I., Stankovic, L.: ‘Fractional fourier transform as a signal processing tool: an overview of recent developments’, Signal Process., 2011, 91, (6), pp. 1351–1369.
  17. 17)
      • 9. Ye, S., Wang, W.: ‘Stability analysis and stabilisation for a class of 2-D nonlinear discrete systems’, Int. J. Syst. Sci., 2011, 42, (5), pp. 839–851.
  18. 18)
      • 16. Ghous, I., Xiang, Z.: ‘H∞ control of a class of 2-D continuous switched delayed systems via state dependent switching’, Int. J. Syst. Sci., 2016, 47, (2), pp. 300–313.
  19. 19)
      • 2. Kaczorek, T.: ‘Two-dimensional linear systems’ (Berlin, Springer, 1985).
  20. 20)
      • 30. Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., et al: ‘Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems’, Commun. Nonlinear Sci. Numer. Simul., 2015, 22, (1–3), pp. 650–659.
  21. 21)
      • 25. Devi, J., Mc Rae, F., Drici, Z.: ‘Variational Lyapunov method for fractional differential equations’, Comput. Math. Appl., 2012, 64, (10), pp. 2982–2989.
  22. 22)
      • 23. Wei, Y., Tse, P.W., Du, B., et al: ‘An innovative fixed-pole numerical approximation for fractional order systems’, ISA Trans., 2016, 62, pp. 94–102.
  23. 23)
      • 10. Yeganefar, N., Yeganefar, N., Ghamgui, M., et al: ‘Lyapunov theory for 2-D nonlinear Roesser models: application to asymptotic and exponential stability’, IEEE Trans. Autom. Control, 2013, 58, (5), pp. 1299–1304.
  24. 24)
      • 39. Chen, H.: ‘Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation’, Int. J. Control Autom. Syst., 2014, 12, (6), pp. 1216–1224.
  25. 25)
      • 34. Deng, W., Li, C., Lu, J.: ‘Stability analysis of linear fractional differential system with multiple time delays’, Nonlinear Dyn., 2007, 48, (4), pp. 409–416.
  26. 26)
      • 37. Ding, D., Qi, D., Peng, J., et al: ‘Asymptotic pseudo-state stabilization of commensurate fractional-order nonlinear systems with additive disturbance’, Nonlinear Dyn., 2015, 81, (1–2), pp. 667–677.
  27. 27)
      • 17. Huang, S., Xiang, Z.: ‘Stability analysis of two-dimensional switched non-linear continuous-time systems’, IET Control Theory Appl., 2016, 10, (6), pp. 724–729.
  28. 28)
      • 29. Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: ‘Lyapunov functions for fractional order systems’, Commun. Nonlinear Sci. Numer. Simul., 2014, 19, (9), pp. 2951–2957.
  29. 29)
      • 3. Lu, W.S., Antoniou, A.: ‘Two-dimensional digital filters’ (Marcel Dekker, New York, 1992).
  30. 30)
      • 31. Wen, Y., Zhou, X.F., Zhang, Z., et al: ‘Lyapunov method for nonlinear fractional differential systems with delay’, Nonlinear Dyn., 2015, 82, (1–2), pp. 1015–1025.
  31. 31)
      • 40. Chen, H., Zhang, J., Chen, B., et al: ‘Global practical stabilization for non-holonomic mobile robots with uncalibrated visual parameters by using a switching controller’, IMA J. Math. Control Inf., 2013, 30, (4), pp. 543–557.
  32. 32)
      • 15. Emelianova, J., Pakshin, P., Galkowski, K., et al: ‘Stability of nonlinear 2-D systems described by the continuous-time Roesser model’, Autom. Remote Control, 2014, 75, (5), pp. 845–858.
  33. 33)
      • 38. Yu, W., Luo, Y., Chen, Y.Q., et al: ‘Frequency domain modelling and control of fractional-order system for permanent magnet synchronous motor velocity servo system’, IET Control Theory Appl., 2016, 10, (2), pp. 136–143.
  34. 34)
      • 27. Burton, T.A.: ‘Fractional differential equations and Lyapunov functionals’, Nonlinear Anal. Theory Methods Appl., 2011, 74, (16), pp. 5648–5662.
  35. 35)
      • 22. Wei, Y., Gao, Q., Peng, C., et al: ‘A rational approximate method to fractional order systems’, Int. J. Control. Autom. Syst., 2014, 12, (6), pp. 1180–1186.
  36. 36)
      • 12. Hmamed, A., Mesquine, F., Tadeo, F., et al: ‘Stabilization of 2D saturated systems by state feedback control’, Multidimen. Syst. Signal Process., 2010, 21, (3), pp. 277–292.
  37. 37)
      • 35. Li, Y., Chen, Y., Podlubny, I.: ‘Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability’, Comput. Math. Appl., 2010, 59, (5), pp. 1810–1821.
  38. 38)
      • 28. Chen, F.L.: ‘A review of existence and stability results for discrete fractional equations’, J. Comput. Appl. Math., 2015, 1, (1), pp. 22–53.
  39. 39)
      • 33. Baleanu, D., Ranjbar, A., Sadati, S., et al: ‘Lyapunov–Krasovskii stability theorem for fractional systems with delay’, Rom. J. Phys., 2011, 56, (5–6), pp. 636–643.
  40. 40)
      • 4. Du, C., Xie, L.: ‘Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach’, IEEE Trans. Circuits Syst., 1999, 46, (11), pp. 1371–1374.
  41. 41)
      • 32. Hu, J., Lu, G., Zhang, S., et al: ‘Lyapunov stability theorem about fractional system without and with delay’, Commun. Nonlinear Sci. Numer. Simul., 2015, 20, (3), pp. 905–913.
  42. 42)
      • 18. Diethelm, K.: ‘The analysis of fractional differential equations’ (Springer-Verlag, Berlin Heidelberg, 2010).
  43. 43)
      • 7. Huang, S., Xiang, Z.: ‘Delay-dependent robust H∞ control for 2-D discrete nonlinear systems with state delays’, Multidimens. Syst. Signal Process., 2014, 25, (4), pp. 775–794.